Motion word problems can look intimidating, and this lesson test lets you practice them in a low-stakes setting. It includes 15 original ASVAB-style questions from the Distance, Rate and Time lesson, featuring one-vehicle problems, objects moving toward or away from each other, catch-up and head-start scenarios, round trips and trips with stops.
A bus travels at 64 kilometers per hour for 2.5 hours. How far does it travel?
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Answer: A
Correct answer: 160 km. Use
d=r×t
64×2.5=160km
A (correct): Distance equals rate times time: 64 times 2.5 is 160 km.
B: This divides the speed by the time instead of multiplying.
C: This uses only 2 hours and drops the half hour.
D: This adds the speed and the time instead of multiplying them.
Question 2 of 15 · easy
A trucker must drive 357 miles at an average speed of 42 miles per hour. How long will the drive take?
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Answer: A
Correct answer: 8 hours 30 minutes. Time = distance divided by rate:
357÷42=8.5hours
Convert the decimal: 0.5 times 60 = 30 minutes, so the drive takes 8 hours 30 minutes.
A (correct): 357 divided by 42 is 8.5 hours, and 0.5 hour is 30 minutes.
B: This reads 8.5 hours as 8 hours 50 minutes instead of converting 0.5 hour to minutes.
C: This divides the speed by the distance instead of the distance by the speed.
D: This reads 0.5 hour as 5 minutes; half an hour is 30 minutes.
Question 3 of 15 · easy
A bike courier covers 34 miles in 40 minutes. What is the courier's average speed in miles per hour?
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Answer: B
Correct answer: 51 mph. Convert the time: 40 minutes is
6040=32hour
Rate:
34÷32=34×23=51miles
per hour.
A: This divides by 40 minutes without converting, which gives miles per minute, not miles per hour.
B (correct): 40 minutes is two-thirds of an hour, and 34 divided by two-thirds is 51 miles per hour.
C: This writes 40 minutes as 0.4 hour instead of two-thirds of an hour.
D: This multiplies 34 by two-thirds instead of dividing by it.
Question 4 of 15 · easy
Two cyclists leave the same corner at the same time and ride in opposite directions, one at 11 miles per hour and the other at 13 miles per hour. How far apart are they after 3 hours?
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Answer: D
Correct answer: 72 miles. Opposite directions, so add the speeds:
11 + 13 = 24 miles
per hour. Distance apart:
24×3=72miles
A: This is how far apart they are after 1 hour, not 3 hours.
B: This counts only the faster cyclist's distance.
C: This subtracts the speeds, which is correct only when both ride in the same direction.
D (correct): Riding apart, they separate at 11 + 13 = 24 miles per hour, and 24 times 3 is 72 miles.
Question 5 of 15 · easy
Two trains are 495 kilometers apart on parallel tracks and head toward each other, one at 75 km/h and the other at 90 km/h. How long until they meet?
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Answer: C
Correct answer: 3 hours. Approaching, so add:
75 + 90 = 165 km
/h. Time:
495÷165=3hours
A: This divides by the slower train's speed alone, as if the other train were standing still.
B: This divides by the faster train's speed alone, as if the other train were standing still.
C (correct): The gap closes at 75 + 90 = 165 km/h, and 495 divided by 165 is 3 hours.
D: This divides by the difference of the speeds; trains moving toward each other close the gap at the sum.
Question 6 of 15 · medium
A moving van traveling at 52 miles per hour is 21 miles ahead of a car traveling the same road in the same direction at 59 miles per hour. How long will it take the car to catch the van?
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Answer: D
Correct answer: 3 hours. Same direction, so subtract:
59 - 52 = 7 miles
per hour. Catch-up time:
21÷7=3hours
A: This adds the speeds; in a chase the gap shrinks by the difference of the speeds.
B: This divides the gap by the van's speed, which does not describe how fast the gap closes.
C: This divides the gap by the car's full speed, ignoring that the van keeps moving.
D (correct): The car gains 59 - 52 = 7 miles per hour, and 21 divided by 7 is 3 hours.
Question 7 of 15 · medium
A truck leaves a warehouse at 40 miles per hour. One hour 30 minutes later, a car leaves the same warehouse on the same road at 55 miles per hour. How long after the car leaves does it catch the truck?
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Answer: B
Correct answer: 4 hours. Lead:
40×1.5=60miles
Gain:
55 - 40 = 15 miles
per hour. Time:
60÷15=4hours
after the car leaves.
A: This adds the speeds; in a chase the gap closes at the difference of the speeds.
B (correct): The truck's lead is 40 times 1.5, or 60 miles, and the car gains 15 miles per hour, so 60 divided by 15 is 4 hours.
C: This measures from when the truck left, but the question asks for time after the car leaves.
D: This divides the 60-mile lead by the car's full speed instead of by the 15 mph it gains.
Question 8 of 15 · medium
A jogger runs 6 miles to a park at 6 miles per hour and runs the same route home at 4 miles per hour. What is her average speed for the round trip?
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Answer: C
Correct answer: 4.8 mph. Times:
6÷6=1hour
out and
6÷4=1.5hours
back. Average speed:
12÷2.5=4.8miles
per hour.
A: This divides the one-way distance of 6 miles by the total time instead of the full 12 miles.
B: This averages the two speeds, but she spends more time at the slower speed.
C (correct): The trip is 12 miles in 1 + 1.5 = 2.5 hours, and 12 divided by 2.5 is 4.8 miles per hour.
D: This adds the two speeds, which is not an average at all.
Question 9 of 15 · medium
A driver goes 110 miles at 55 miles per hour, stops for 30 minutes, then drives 2.5 more hours at 52 miles per hour. What is her overall average speed for the trip, including the stop?
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Answer: B
Correct answer: 48 mph. Distance: 110 + 52×2.5 =
110 + 130 = 240 miles
Time:
110÷55=2hours
plus 0.5 hour stopped, plus 2.5 hours, for 5 hours. Average:
240÷5=48miles
per hour.
A: This divides 240 miles by 4 hours, leaving out half an hour of driving.
B (correct): She covers 110 + 130 = 240 miles in 2 + 0.5 + 2.5 = 5 hours, and 240 divided by 5 is 48 miles per hour.
C: This averages the two speeds instead of dividing total distance by total time.
D: This leaves the 30-minute stop out of the total time, but the question says to include it.
Question 10 of 15 · medium
Two cities are 380 miles apart. Car A leaves one city at 9:00 a.m. traveling at 50 miles per hour toward the other city. Car B leaves the other city at 10:00 a.m. traveling toward Car A at 60 miles per hour. At what time do the cars meet?
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Answer: B
Correct answer: 1:00 p.m. In the first hour Car A covers 50 miles, so the gap at 10:00 a.m. is
380 - 50 = 330 miles
Closing speed:
50 + 60 = 110 miles
per hour. Time:
330÷110=3hours
after 10:00 a.m., which is 1:00 p.m.
A: This ignores the 50 miles Car A covers before Car B starts and divides the full 380 miles by 110.
B (correct): By 10:00 a.m. Car A has gone 50 miles, leaving 330 miles that close at 110 miles per hour, which takes 3 hours from 10:00 a.m.
C: This treats both cars as leaving at 9:00 a.m., ignoring Car B's later start.
D: This finds the 3 hours correctly but counts them from Car A's 9:00 a.m. start instead of from 10:00 a.m.
Question 11 of 15 · medium
A commuter train runs at 84 kilometers per hour for 35 minutes. How far does it travel?
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Answer: D
Correct answer: 49 km. Convert the time to hours, then multiply:
84×6035=49km
A: This divides the speed by the number of minutes.
B: This writes 35 minutes as 0.35 hour instead of 35/60 of an hour.
C: This multiplies the speed by 35 minutes without converting the minutes to hours.
D (correct): 35 minutes is 35/60 of an hour, and 84 times 35/60 is 49 km.
Question 12 of 15 · hard
A fishing boat leaves a dock at 18 miles per hour. Fifty minutes later, a patrol boat leaves the same dock on the same course at 30 miles per hour. How far from the dock is the patrol boat when it catches the fishing boat?
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Answer: A
Correct answer: 37.5 miles. Lead:
18×6050=15miles
Gain:
30 - 18 = 12 mph
so the chase lasts
15÷12=1.25hours
Distance from the dock:
30×1.25=37.5miles
A (correct): The fishing boat's lead is 15 miles, the patrol boat gains 12 mph, so it takes 1.25 hours and travels 30 times 1.25, or 37.5 miles.
B: This adds the 15-mile lead to the patrol boat's distance, counting the lead twice.
C: This is the fishing boat's head start, not where the boats meet.
D: This is how far the fishing boat travels during the 1.25-hour chase, leaving out its 15-mile lead.
Question 13 of 15 · hard
A delivery drone flies 12 km to a drop-off point at 36 km/h, hovers there for 10 minutes, and flies the 12 km back into a headwind at 24 km/h. What is its average speed for the whole trip, including the hover?
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Answer: C
Correct answer: 24 km/h. Out:
12÷36=31hour
(20 minutes). Back:
12÷24=21hour
(30 minutes). Add the 10-minute hover: 60 minutes, or 1 hour, for 24 km. Average:
24÷1=24km
/h.
A: This uses only flying time and leaves out the 10-minute hover the question includes.
B: This divides only the one-way distance of 12 km by the total time.
C (correct): Flight times are 20 and 30 minutes; with the 10-minute hover the trip takes 1 hour for 24 km, so the average is 24 km/h.
D: This averages the two flying speeds, ignoring both the longer slow leg and the hover.
Question 14 of 15 · hard
Two runners start at opposite ends of a 15-mile trail and run toward each other. Runner A starts at 7:00 a.m. at 6 miles per hour. Runner B starts at 7:30 a.m. at 4 miles per hour. How far from her starting point is Runner A when they meet?
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Answer: D
Correct answer: 10.2 miles. By 7:30 Runner A has gone
6×0.5=3miles
leaving a 12-mile gap. Closing speed:
6 + 4 = 10 mph
so they meet
12÷10=1.2hours
later. Runner A's distance:
3+6×1.2=10.2miles
A: This counts only Runner A's distance after Runner B starts and leaves out her first 3 miles.
B: This ignores Runner B's late start, as if both had started at 7:00 a.m.
C: This is Runner B's distance from her own starting point, not Runner A's.
D (correct): A runs 3 miles alone, leaving 12 miles that close at 10 mph in 1.2 hours; A then adds 7.2 miles, for 10.2 miles total.
Question 15 of 15 · hard
A driver wants to average 50 miles per hour for a 200-mile trip. She drives the first 120 miles at 40 miles per hour. How fast must she drive the remaining 80 miles to reach her goal?
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Answer: C
Correct answer: 80 mph. Total time allowed:
200÷50=4hours
Time used:
120÷40=3hours
Remaining: 80 miles in 1 hour, so she must drive 80 miles per hour.
A: This divides the remaining 80 miles by the 3 hours already used instead of by the 1 hour left.
B: This assumes the two speeds must average 50, but average speed is total distance over total time.
C (correct): The trip may take 200 divided by 50, or 4 hours; the first leg used 3 hours, so 80 miles must be covered in 1 hour.
D: Driving the rest at 50 mph would leave the overall average below 50, because the first leg was slower.
A mountain biker rides a 30-mile course made of three 10-mile sections. She rides the first section at 10 mph, the climb at 15 mph and the downhill finish at 30 mph. What is her average speed for the whole course?
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Answer: D
Correct answer: 15 mph. Find each section's time:
10 ÷ 10 = 1 hour
10 ÷ 15 = 2/3 hour
(40 minutes) and
10 ÷ 30 = 1/3 hour
(20 minutes). The total time is 2 hours, so the average speed is
30 ÷ 2 = 15 mph
Averaging the three speeds fails because she spends far more time on the slow section.
A: This is the simple mean of 10, 15 and 30, which ignores that the slow section takes the most time.
B: This comes from writing 40 minutes as 0.4 hour and 20 minutes as 0.2 hour, which makes the total time look like 1.6 hours.
C: This averages only the slowest and fastest speeds and still ignores how long each section takes.
D (correct): Total distance 30 miles divided by total time 2 hours gives 15 mph.
Practice 2 of 35 · easy
A military convoy travels at a steady 38 miles per hour for 3.5 hours. How far does the convoy travel?
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Answer: B
Correct answer: 133 miles. Distance equals rate times time:
38 × 3.5 = 133 miles
The first 3 hours give 114 miles and the extra half hour adds
38 × 0.5 = 19 miles
A: This uses only 3 hours and drops the extra half hour of driving.
B (correct): Multiplying 38 mph by 3.5 hours gives 133 miles.
C: This rounds the time up to 4 hours before multiplying.
D: This adds the speed and the time instead of multiplying them.
Practice 3 of 35 · hard
A supply truck leaves a base at 7:00 a.m. traveling 36 mph. At 7:50 a.m., a jeep leaves the same base on the same road traveling 51 mph. At what time does the jeep catch the truck?
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Answer: A
Correct answer: 9:50 a.m. First turn the 50-minute head start into distance:
36 × 50/60 = 30 miles
The jeep gains
51 − 36 = 15 miles
each hour, so it needs
30 ÷ 15 = 2 hours
Two hours after 7:50 a.m. is 9:50 a.m.
A (correct): The 30-mile lead closes at 15 mph in 2 hours, counted from the jeep's 7:50 a.m. start.
B: This finds the 2-hour chase time but adds it to the truck's 7:00 a.m. start instead of the jeep's start.
C: This treats 50 minutes as 0.5 hour, giving an 18-mile lead and a 72-minute chase.
D: This divides the 30-mile lead by the jeep's full speed of 51 mph instead of by the 15 mph it gains.
Practice 4 of 35 · medium
A harbor patrol boat covers 39 miles in 1 hour 12 minutes. What is the boat's average speed?
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Answer: D
Correct answer: 32.5 mph. Write the time in hours: 12 minutes is
12/60 = 0.2 hour
so the time is 1.2 hours. Then speed = distance ÷ time =
39 ÷ 1.2 = 32.5 mph
A: This writes 1 hour 12 minutes as 1.12 hours instead of converting the minutes to 0.2 hour.
B: This multiplies the distance by the time instead of dividing.
C: This ignores the extra 12 minutes and divides by 1 hour.
D (correct): With the time written as 1.2 hours, 39 ÷ 1.2 = 32.5 mph.
Practice 5 of 35 · easy
A canoeist paddles 13.5 miles down a river at a steady 3 miles per hour. How long does the trip take?
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Answer: D
Correct answer: 4 hours 30 minutes. Time equals distance divided by speed:
13.5 ÷ 3 = 4.5 hours
The 0.5 hour is
0.5 × 60 = 30 minutes
so the trip takes 4 hours 30 minutes.
A: This reads the decimal 0.5 hour as 50 minutes instead of multiplying it by 60.
B: This reads the decimal 0.5 hour as 5 minutes instead of 30 minutes.
C: This multiplies 13.5 by 3 instead of dividing the distance by the speed.
D (correct): 13.5 ÷ 3 = 4.5 hours, and half an hour is 30 minutes.
Practice 6 of 35 · medium
A family leaves home at 7:30 a.m. and drives 189 miles to a lake cabin at an average speed of 54 mph. At what time do they arrive?
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Answer: B
Correct answer: 11:00 a.m. Driving time is
189 ÷ 54 = 3.5 hours
which is 3 hours 30 minutes. Adding 3 hours 30 minutes to 7:30 a.m. gives 11:00 a.m.
A: This reads 3.5 hours as 3 hours 50 minutes.
B (correct): The trip lasts 3.5 hours, or 3 hours 30 minutes, and 7:30 a.m. plus that time is 11:00 a.m.
C: This reads 3.5 hours as 3 hours 5 minutes.
D: This drops the half hour and adds only 3 hours.
Practice 7 of 35 · medium
At noon, two helicopters lift off from the same base. One flies due north at 120 mph and the other flies due south at 150 mph. At what time will they be 540 miles apart?
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Answer: C
Correct answer: 2:00 p.m. Moving in opposite directions, they separate at
120 + 150 = 270 miles
per hour. Time =
540 ÷ 270 = 2 hours
so they are 540 miles apart at 2:00 p.m.
A: This uses only the slower helicopter's speed: 540 ÷ 120 = 4.5 hours.
B: This uses only the faster helicopter's speed: 540 ÷ 150 = 3.6 hours.
C (correct): They separate at 270 mph, and 540 ÷ 270 = 2 hours after noon.
D: This subtracts the speeds to get 30 mph, which applies to a chase, not to opposite directions.
Practice 8 of 35 · medium
Two survey crews are 22 miles apart on a straight pipeline route and walk toward each other, one crew at 3 mph and the other at 2.5 mph. How far has the faster crew walked when they meet?
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Answer: A
Correct answer: 12 miles. The gap closes at
3 + 2.5 = 5.5 miles
per hour, so they meet after
22 ÷ 5.5 = 4 hours
In that time the faster crew walks
3 × 4 = 12 miles
(and the slower crew walks the other 10).
A (correct): They meet after 4 hours, and the faster crew walks 3 × 4 = 12 miles.
B: This is how far the slower crew walks, 2.5 × 4.
C: This assumes they meet halfway, which happens only if their speeds are equal.
D: This multiplies the faster speed by the closing speed (3 × 5.5) instead of by the meeting time.
Practice 9 of 35 · medium
A highway patrol car traveling 70 mph is chasing a car that is 6 miles ahead and moving at 62 mph in the same direction. How far does the patrol car travel before it catches up?
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Answer: C
Correct answer: 52.5 miles. The patrol car gains
70 − 62 = 8 miles
per hour, so it closes the 6-mile gap in
6 ÷ 8 = 0.75 hour
In that time it travels
70 × 0.75 = 52.5 miles
A: This is the distance the car ahead travels, 62 × 0.75, not the patrol car's distance.
B: This adds the 6-mile lead to the patrol car's distance a second time.
C (correct): The catch-up takes 0.75 hour, and 70 × 0.75 = 52.5 miles.
D: This adds the speeds to get 132 mph, which is the rule for vehicles approaching each other, not for a chase.
Practice 10 of 35 · medium
A cyclist leaves a campground riding at 10 mph. Forty-five minutes later, her friend leaves the same campground on the same trail riding at 16 mph. How long after the friend starts does she catch up?
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Answer: D
Correct answer: 1 hour 15 minutes. Turn the time head start into distance:
10 × 0.75 = 7.5 miles
The friend gains
16 − 10 = 6 miles
each hour, so she needs
7.5 ÷ 6 = 1.25 hours
which is 1 hour 15 minutes.
A: This reads 1.25 hours as 1 hour 25 minutes instead of converting 0.25 hour to 15 minutes.
B: This is the time measured from the first cyclist's start, not from the friend's start.
C: This divides the 7.5-mile lead by the friend's full speed of 16 mph instead of by the 6 mph she gains.
D (correct): A 7.5-mile lead closed at 6 mph takes 1.25 hours, or 1 hour 15 minutes.
Practice 11 of 35 · hard
Two towns are 207 miles apart. Car A leaves the first town at 1:00 p.m. traveling 48 mph toward the second town. At 1:45 p.m., Car B leaves the second town traveling 60 mph toward Car A. At what time do the cars meet?
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Answer: B
Correct answer: 3:20 p.m. By 1:45 p.m. Car A has driven
48 × 0.75 = 36 miles
leaving a 171-mile gap. Together the cars close
48 + 60 = 108 miles
per hour, so they need
171 ÷ 108 = 1
7/12 hours, which is 1 hour 35 minutes. That is 1 hour 35 minutes after 1:45 p.m., or 3:20 p.m.
A: This divides the full 207 miles by 108 mph as if both cars started at 1:00 p.m.
B (correct): The 171-mile gap left at 1:45 p.m. closes at 108 mph in 1 hour 35 minutes.
C: This finds the 1 hour 35 minutes correctly but counts it from Car A's 1:00 p.m. start.
D: This reads about 1.58 hours as 1 hour 58 minutes instead of 1 hour 35 minutes.
Practice 12 of 35 · easy
A ferry crosses a 27-mile stretch of water in 1 hour 30 minutes. What is the ferry's average speed?
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Answer: B
Correct answer: 18 mph. Write the time as a decimal: 1 hour 30 minutes = 1.5 hours. Speed = distance ÷ time =
27 ÷ 1.5 = 18 mph
A: This multiplies the distance by the time instead of dividing.
B (correct): Dividing 27 miles by 1.5 hours gives 18 mph.
C: This writes 1 hour 30 minutes as 1.3 hours instead of 1.5 hours.
D: This rounds the time up to 2 hours before dividing.
Practice 13 of 35 · medium
Two towns are 335 miles apart. A truck leaves the first town at 7:00 a.m. traveling 55 mph toward the second town. At 8:00 a.m., a car leaves the second town traveling 85 mph toward the truck. How far from the first town do they meet?
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Answer: D
Correct answer: 165 miles. By 8:00 a.m. the truck has gone 55 miles, leaving a 280-mile gap. The gap closes at
55 + 85 = 140 mph
so they meet
280 ÷ 140 = 2 hours
after the car starts. The truck has then driven 3 hours, or
55 × 3 = 165 miles
from the first town.
A: This counts only the 2 hours after the car starts and forgets the truck's first hour.
B: This is the car's distance from the second town, 85 × 2.
C: This assumes they meet halfway between the towns, which ignores their different speeds and start times.
D (correct): The truck drives 3 hours in all at 55 mph, which is 165 miles.
Practice 14 of 35 · medium
An electrician drives 45 miles to a job site at 60 mph and returns home along the same road at 45 mph. How much longer does the return trip take than the trip out?
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Answer: C
Correct answer: 15 minutes. Treat each leg separately. Out:
45 ÷ 60 = 0.75 hour
(45 minutes). Back:
45 ÷ 45 = 1 hour
(60 minutes). The return trip takes
60 − 45 = 15 minutes
longer.
A: This reads the 0.25-hour difference as 25 minutes instead of 15 minutes.
B: This is the total time for both legs, not the difference between them.
C (correct): The trip out takes 45 minutes and the trip back takes 60 minutes, a difference of 15 minutes.
D: This is the time for the trip out, not how much longer the return takes.
Practice 15 of 35 · easy
Two search teams leave a base camp at the same time and walk in opposite directions, one at 2.5 mph and the other at 3.5 mph. How far apart are they after 4 hours?
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Answer: B
Correct answer: 24 miles. Moving apart, they separate at
2.5 + 3.5 = 6 miles
per hour. After 4 hours they are
6 × 4 = 24 miles
apart.
A: This subtracts the speeds, which is the rule for a chase, not for opposite directions.
B (correct): They separate at 6 mph, and 6 × 4 = 24 miles.
C: This counts only the faster team's distance, 3.5 × 4.
D: This finds the combined speed but forgets to multiply by the 4 hours.
Practice 16 of 35 · easy
Two delivery vans are 270 miles apart on the same highway and drive toward each other, one at 50 mph and the other at 40 mph. How long until they meet?
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Answer: C
Correct answer: 3 hours. When two vehicles approach each other, the gap closes at the sum of their speeds:
50 + 40 = 90 mph
Time =
270 ÷ 90 = 3 hours
A: This uses the difference of the speeds, 10 mph, which applies only to a chase.
B: This divides by the faster van's speed alone and ignores the other van.
C (correct): The gap closes at 90 mph, and 270 ÷ 90 = 3 hours.
D: This divides by the slower van's speed alone and ignores the other van.
Practice 17 of 35 · easy
A tractor-trailer traveling 44 mph is 12 miles ahead of a motorcycle traveling the same road in the same direction at 60 mph. How long will it take the motorcycle to catch the truck?
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Answer: A
Correct answer: 45 minutes. In a chase the gap shrinks by the difference of the speeds:
60 − 44 = 16 mph
Time =
12 ÷ 16 = 0.75 hour
and
0.75 × 60 = 45 minutes
A (correct): The motorcycle gains 16 mph, so 12 ÷ 16 = 0.75 hour, which is 45 minutes.
B: This adds the speeds to get 104 mph, which is the rule for vehicles moving toward each other.
C: This divides the gap by the motorcycle's full speed of 60 mph instead of by the 16 mph it gains.
D: This reads 0.75 hour as 75 minutes instead of multiplying by 60.
Practice 18 of 35 · medium
A tour bus drives for 2 hours at 45 mph and then for 3 hours at 60 mph. What is the bus's average speed for the 5 hours?
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Answer: C
Correct answer: 54 mph. Find the total distance:
45 × 2 = 90 miles
and
60 × 3 = 180 miles
so 270 miles in all. Average speed =
270 ÷ 5 = 54 mph
More time was spent at 60 mph, so the average is above the simple mean of the two speeds.
A: This is the simple mean of 45 and 60, which ignores that the bus spent longer at 60 mph.
B: This swaps the times, giving 3 hours at 45 mph and 2 hours at 60 mph.
C (correct): Total distance 270 miles divided by total time 5 hours gives 54 mph.
D: This uses only the speed of the longer leg and ignores the slower 2 hours.
Practice 19 of 35 · medium
A family drives 2.5 hours at 58 mph, stops 45 minutes for lunch, then drives 1.75 hours at 60 mph. What is the overall average speed for the trip, including the lunch stop?
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Answer: A
Correct answer: 50 mph. Distance:
58 × 2.5 = 145 miles
and
60 × 1.75 = 105 miles
so 250 miles. Time:
2.5 + 0.75 + 1.75 = 5 hours
because the stop adds time but no distance. Average speed =
250 ÷ 5 = 50 mph
A (correct): The trip covers 250 miles in 5 hours, counting the 0.75-hour stop.
B: This simply averages 58 and 60 and leaves out the stop entirely.
C: This divides 250 miles by 4.25 hours of driving and forgets to add the lunch stop.
D: This writes 45 minutes as 0.45 hour instead of 0.75 hour.
Practice 20 of 35 · medium
A recruit runs at a steady 7.5 miles per hour. How many minutes does it take the recruit to run 3 miles?
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Answer: D
Correct answer: 24 minutes. Time = distance ÷ speed =
3 ÷ 7.5 = 0.4 hour
Convert to minutes:
0.4 × 60 = 24 minutes
A: This multiplies the distance by the speed instead of dividing.
B: This reads 0.4 hour as 40 minutes instead of multiplying by 60.
C: This divides the speed by the distance, turning the formula upside down.
D (correct): 3 ÷ 7.5 = 0.4 hour, and 0.4 × 60 = 24 minutes.
Practice 21 of 35 · medium
A freight train leaves a rail yard at 1:00 p.m. traveling 30 mph. At 3:00 p.m., an express train leaves the same yard on a parallel track in the same direction at 50 mph. At what time does the express catch up with the freight?
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Answer: C
Correct answer: 6:00 p.m. By 3:00 p.m. the freight has a lead of
30 × 2 = 60 miles
The express gains
50 − 30 = 20 miles
each hour, so it needs
60 ÷ 20 = 3 hours
Three hours after 3:00 p.m. is 6:00 p.m.
A: This adds the speeds to get 80 mph, which is the rule for trains moving toward each other.
B: This finds the 3-hour chase time but counts it from the freight's 1:00 p.m. start.
C (correct): The 60-mile lead closes at 20 mph in 3 hours, counted from 3:00 p.m.
D: This divides the 60-mile lead by the express's full speed of 50 mph instead of by the 20 mph it gains.
Practice 22 of 35 · easy
A survey drone flies at 48 km/h for 15 minutes. How far does it fly?
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Answer: D
Correct answer: 12 km. The speed is per hour, so change the time to hours first: 15 minutes =
15/60 = 0.25 hour
Distance =
48 × 0.25 = 12 km
A: This multiplies 48 by 15 without changing minutes to hours.
B: This divides the speed by the number of minutes.
C: This writes 15 minutes as 0.15 hour instead of 0.25 hour.
D (correct): 15 minutes is 0.25 hour, and 48 × 0.25 = 12 km.
Practice 23 of 35 · hard
A kayaker paddles from a beach to an island at 6 mph and returns along the same route at 4 mph. The round trip takes 2.5 hours. How far is the island from the beach?
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Answer: B
Correct answer: 6 miles. Let d be the one-way distance. The time out is d/6 and the time back is d/4, and together they make 2.5 hours:
6d+4d=2.5
With a common denominator this is
5d/12 = 2.5
so d = 6 miles. Check: 1 hour out plus 1.5 hours back is 2.5 hours.
A: This is the round-trip distance, not the distance from the beach to the island.
B (correct): Six miles takes 1 hour out and 1.5 hours back, exactly 2.5 hours.
C: This uses the simple mean speed of 5 mph for the whole trip, which overstates the true average.
D: This assumes the faster speed of 6 mph for the whole trip and then halves the result.
Practice 24 of 35 · medium
A dump truck hauls gravel 24 miles to a site at 40 mph and returns empty along the same road at 60 mph. What is the truck's average speed for the round trip?
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Answer: B
Correct answer: 48 mph. Out:
24 ÷ 40 = 0.6 hour
Back:
24 ÷ 60 = 0.4 hour
The truck covers 48 miles in 1 hour, so its average speed is 48 mph. With equal distances the average is pulled toward the slower speed.
A: This is the simple mean of 40 and 60, which ignores the extra time spent at the slower speed.
B (correct): Total distance 48 miles divided by total time 1 hour gives 48 mph.
C: This divides only the one-way distance by the total time.
D: This adds the two speeds instead of dividing total distance by total time.
Practice 25 of 35 · medium
A sales representative drives 150 miles to a client at 60 mph and returns on the same road. The whole round trip takes 5.5 hours of driving. What was her average speed on the return trip?
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Answer: D
Correct answer: 50 mph. The trip out takes
150 ÷ 60 = 2.5 hours
so the return takes
5.5 − 2.5 = 3 hours
Return speed =
150 ÷ 3 = 50 mph
A: This is the average speed for the whole round trip, 300 ÷ 5.5, not the return speed.
B: This divides one leg's 150 miles by the full round-trip time of 5.5 hours.
C: This wrongly assumes the round-trip average is the simple mean of the two leg speeds.
D (correct): The return leg takes 3 hours, and 150 ÷ 3 = 50 mph.
Practice 26 of 35 · medium
Two motorcycles leave the same gas station at the same time and ride in the same direction on a highway, one at 65 mph and the other at 50 mph. After how long will they be 36 miles apart?
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Answer: A
Correct answer: 2 hours 24 minutes. Moving the same way, the gap grows by the difference of the speeds:
65 − 50 = 15 mph
Time =
36 ÷ 15 = 2.4 hours
Since
0.4 × 60 = 24 minutes
that is 2 hours 24 minutes.
A (correct): The gap grows 15 miles each hour, and 36 ÷ 15 = 2.4 hours, or 2 hours 24 minutes.
B: This reads 2.4 hours as 2 hours 40 minutes instead of converting 0.4 hour to 24 minutes.
C: This adds the speeds, which applies only when the riders head in opposite directions.
D: This divides 36 miles by the faster rider's speed alone, as if the other rider stood still.
Practice 27 of 35 · hard
A jogger leaves a trailhead running 5 mph. Thirty minutes later, a cyclist leaves the same trailhead on the same path riding 13 mph. How far apart are they 1 hour after the cyclist starts?
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Answer: D
Correct answer: 5.5 miles. One hour after the cyclist starts, she has gone
13 × 1 = 13 miles
The jogger has then run for 1.5 hours, covering
5 × 1.5 = 7.5 miles
They are
13 − 7.5 = 5.5 miles
apart, with the cyclist ahead.
A: This uses the 8 mph difference for 1 hour but ignores the jogger's 2.5-mile head start.
B: This adds the jogger's 2.5-mile head start to the gap instead of subtracting it.
C: This adds the two distances as if they had traveled in opposite directions.
D (correct): The cyclist is at 13 miles and the jogger is at 7.5 miles, so they are 5.5 miles apart.
Practice 28 of 35 · hard
Two hikers start at opposite ends of a 22.5-mile trail at 8:00 a.m. and walk toward each other, one at 4 mph and the other at 3 mph. After 2 hours, the faster hiker rests for 30 minutes while the slower hiker keeps walking. At what time do they meet?
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Answer: C
Correct answer: 11:30 a.m. In the first 2 hours they close
7 × 2 = 14 miles
leaving 8.5 miles. During the 30-minute rest only the slower hiker moves, closing
3 × 0.5 = 1.5 miles
and leaving 7 miles. Walking together again they close 7 mph, so they need 1 more hour. Total time is
2 + 0.5 + 1 = 3.5 hours
so they meet at 11:30 a.m.
A: This ignores the rest and divides the whole 22.5 miles by 7 mph.
B: This treats the rest as stopping both hikers, so no distance is closed during those 30 minutes.
C (correct): The meeting comes 3.5 hours after the start once the rest and the slower hiker's progress during it are counted.
D: This ignores the rest and also reads 3.21 hours as 3 hours 21 minutes.
Practice 29 of 35 · easy
A train travels 225 miles in 3 hours. At the same rate, how far will it travel in 5 hours?
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Answer: A
Correct answer: 375 miles. First find the rate:
225 ÷ 3 = 75 mph
Then distance =
75 × 5 = 375 miles
A (correct): The train's rate is 75 mph, and 75 × 5 = 375 miles.
B: This sets up the proportion upside down, multiplying 225 by 3/5 instead of 5/3.
C: This doubles 225 miles, as if 5 hours were twice as long as 3 hours.
D: This adds one hour's distance of 75 miles to 225 instead of adding two hours' worth.
Practice 30 of 35 · hard
Two cargo planes are 1,350 miles apart and fly directly toward each other, one at 300 mph and the other at 240 mph. How far apart are they 1 hour before they meet?
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Answer: A
Correct answer: 540 miles. The gap closes at
300 + 240 = 540 miles
per hour. In the final hour before meeting they close exactly 540 miles, so 1 hour before they meet they are 540 miles apart. Check: they meet after
1,350 ÷ 540 = 2.5 hours
and at 1.5 hours they have covered 810 miles, leaving 540.
A (correct): In the last hour they close the gap at their combined speed of 540 mph.
B: This is how far the two planes have flown together by that time, not the gap still between them.
C: This uses the difference of the speeds, which applies only when one plane chases the other.
D: This counts only the faster plane's last hour and forgets that the other plane is also closing the gap.
Practice 31 of 35 · medium
A long-haul driver must cover 238 miles at an average driving speed of 56 mph and plans to take two 15-minute breaks. How long will the whole trip take, including the breaks?
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Answer: B
Correct answer: 4 hours 45 minutes. Driving time is
238 ÷ 56 = 4.25 hours
which is 4 hours 15 minutes. The two breaks add 30 minutes, so the whole trip takes 4 hours 45 minutes.
A: This is the driving time alone and leaves out both breaks.
B (correct): Driving takes 4 hours 15 minutes, and the two breaks add 30 minutes.
C: This adds only one 15-minute break to the driving time.
D: This reads 4.25 hours as 4 hours 25 minutes before adding the breaks.
Practice 32 of 35 · easy
A courier drives 150 miles in 3 hours in the morning and 90 miles in 2 hours in the afternoon. What is the courier's average speed for all of the day's driving?
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Answer: A
Correct answer: 48 mph. Add distances and times first:
150 + 90 = 240 milesin
3 + 2 = 5 hours
Average speed =
240 ÷ 5 = 48 mph
A (correct): Total distance 240 miles divided by total time 5 hours gives 48 mph.
B: This averages the two speeds, 50 and 45 mph, instead of dividing total distance by total time.
C: This adds the morning and afternoon speeds together.
D: This divides the total distance by only the morning's 3 hours.
Practice 33 of 35 · hard
Two runners start side by side on a 400-meter track and run in the same direction, one at 5 meters per second and the other at 4.2 meters per second. How long until the faster runner first laps the slower one?
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Answer: B
Correct answer: 8 minutes 20 seconds. To lap the slower runner, the faster one must gain a full 400 meters. She gains
5 − 4.2 = 0.8
meter each second, so it takes
400 ÷ 0.8 = 500 seconds
Since 480 seconds is 8 minutes, 500 seconds is 8 minutes 20 seconds.
A: This adds the speeds, which applies only to runners heading toward each other.
B (correct): The faster runner gains 0.8 m/s, so a 400-meter gain takes 500 seconds.
C: This is how long the faster runner takes to run one lap, not how long she takes to gain a lap.
D: This reads 8.33 minutes as 8 minutes 33 seconds instead of converting 0.33 minute to 20 seconds.
Practice 34 of 35 · medium
An electric scooter covers 0.6 mile in 2 minutes. What is its speed in miles per hour?
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Answer: C
Correct answer: 18 mph. Its speed is
0.6 ÷ 2 = 0.3
mile per minute. An hour has 60 minutes, so the speed is
0.3 × 60 = 18 mph
A: This is the speed in miles per minute, not miles per hour.
B: This multiplies 0.6 by 60 but forgets the trip took 2 minutes, not 1.
C (correct): 0.3 mile per minute times 60 minutes gives 18 miles per hour.
D: This multiplies by the 2 minutes instead of dividing by them.
Practice 35 of 35 · hard
A cargo plane flies to a remote airstrip at 200 mph and returns along the same route at 300 mph. The round trip takes 5 hours of flying. How long was the flight out?
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Answer: C
Correct answer: 3 hours. Let d be the one-way distance:
200d+300d=5
Using 600 as the common denominator,
5d/600 = 5
so d = 600 miles. The flight out took
600 ÷ 200 = 3 hours
(and the return took 2 hours).
A: This splits the 5 hours evenly, but the slower leg takes longer.
B: This is the time for the faster return flight, not the flight out.
C (correct): The airstrip is 600 miles away, and 600 ÷ 200 = 3 hours.
D: This uses the simple mean of 250 mph for the round trip, which is not the true average speed.
About this test
Explanations accompany every answer and usually lay the information out in a motion table with rate, time and distance for each traveler. Seeing that structure repeatedly is one of the fastest ways to make these problems routine.
Check which situations caused errors. Misses on round-trip speed point to the equal-distance average-speed trap section; misses on catch-up or meeting items point to the relative-speed shortcut and head-start sections. You can follow up with 35 extra practice questions for this lesson. The accuracy you earn here is for practice tracking and is not an ASVAB or AFQT score.
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