AR · 8 cards

Distance, Rate and Time flashcards

8 cards with the formulas, rules and traps from this lesson. Answer in your head, then flip to check.

Formula · 1/8
What is the motion formula, and what does it assume?
$d = r \times t$ : distance equals rate times time. Know any two to find the third. It assumes a steady speed, or uses the average speed over the trip.
Common trap · 2/8
A train runs 72 km/h for 25 minutes. How far does it go?
Convert time to hours first: $72 \times \frac{25}{60} = 30$ km. Multiplying 72 by 25 directly gives an impossible 1,800.
Rule · 3/8
How do you express 5.5 hours in hours and minutes?
Multiply the decimal part of the hour by 60: $0.5 \times 60 = 30$ , so 5 hours 30 minutes.
Rule · 4/8
What is the relative speed of two travelers, and how is it used?
The sum of their speeds when approaching or moving apart, the difference in a same-direction chase. Time = gap divided by relative speed: a 57 mph car closes an 18-mile gap on a 48 mph bus in $18 \div 9 = 2$ hours.
Strategy · 5/8
How do you handle a head start given as time instead of distance?
Turn it into a lead distance. A 45 mph truck leaving 40 minutes early leads by $45 \times \frac{40}{60} = 30$ miles; a 60 mph car gains 15 mph, so it catches up in 2 hours.
Formula · 6/8
Average speed for two equal-distance legs at speeds a and b?
$\frac{2 ab}{a + b}$ . At 30 mph and 60 mph: $\frac{2 \times 30 \times 60}{90} = 40$ mph, not 45. The slower leg takes longer, so the average leans toward the slower speed.
Rule · 7/8
How does a rest stop affect the overall average speed?
Add the stop to total time but add no distance. 104 miles in 2 hours, a 30-minute stop, then 90 miles in 1.5 hours gives $194 \div 4 = 48.5$ mph.
Strategy · 8/8
Towns 260 mi apart: A leaves at 40 mph, B an hour later at 70 mph. Meeting time?
First remove A's early distance: $260 - 40 = 220$ miles. They close at 110 mph, so they meet 2 hours after B starts, which is 3 hours after A starts.

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