Work and Combined-Rate Problems Lesson Test

Answer: A

Correct answer: 5/8. Each hour the landscaper mows $\frac{1}{8}$ of the park, so 3 hours of work covers $\frac{3}{8}$. The part still unmowed is

• A (correct): Work done is 3/8, and subtracting it from the whole park leaves 5/8.
• B: This is the part already mowed, not the part that remains.
• C: This is the amount mowed in a single hour, not the unmowed fraction.
• D: This compares hours worked to hours left instead of measuring work against the whole job.

Answer: C

Correct answer: 3 hours. Add the hourly rates:

of the batch per hour. Inverting gives 3 hours.

• A: Averaging the times ignores that the team is faster than the faster clerk.
• B: Adding the two times makes the team slower than either clerk, which cannot happen.
• C (correct): The combined rate is 1/3 of the batch per hour, so the job takes 3 hours.
• D: This is the combined rate per hour; it still has to be inverted to get the time.

Answer: B

Correct answer: 6 hours. The hose adds $\frac{1}{4}$ per hour and the leak removes $\frac{1}{12}$ per hour. Net rate:

pond per hour, so filling takes 6 hours.

• A: Adding the leak's rate treats it as a second hose instead of subtracting it.
• B (correct): The net filling rate is 1/12 subtracted from 1/4, which is 1/6 pond per hour, giving 6 hours.
• C: Adding the two times does not account for how the hose and leak work against each other.
• D: Subtracting the times (12 − 4) does not combine the rates properly.

Answer: B

Correct answer: 70 labels per minute. Machine A prints

labels per minute and Machine B prints

labels per minute. Together they print

labels per minute.

• A: Subtracting the two rates is what an opposing process needs, but both machines are adding labels.
• B (correct): Each machine's rate is found first (45 and 25 labels per minute) and then the rates are added.
• C: Adding the label counts gives total output from two different time periods, not a rate per minute.
• D: Dividing the total labels, 330, by the total minutes, 10, mixes the two machines' different run times.

Answer: C

Correct answer: 3.4 hours. Working together must be faster than the faster worker alone, so the time is under 6 hours. It is at least half of 6 hours, or 3 hours. Only 3.4 hours lies between 3 and 6 hours; the exact value is 24/7, about 3.4 hours.

• A: This is the average of the two times, but a team is always faster than its faster member.
• B: Adding the times makes the team slower than either person alone.
• C (correct): This falls between half the faster time (3 hours) and the faster time (6 hours), and it matches the exact value of 24/7 hours.
• D: Even two workers as fast as the carpenter would need 3 hours, so 2.5 hours is too short.

Answer: A

Correct answer: 7 hours 12 minutes. Use the common denominator 36:

per hour. The time is

Since 0.2 hour is 12 minutes, that is 7 hours 12 minutes.

• A (correct): The combined rate is 5/36 per hour, so the time is 36/5 = 7.2 hours, and 0.2 hour equals 12 minutes.
• B: Averaging the two times ignores that both pumps work at once.
• C: Adding the times would make two pumps slower than one.
• D: This reads 0.2 hour as 20 minutes; 0.2 of 60 minutes is only 12 minutes.

Answer: D

Correct answer: 1 hour 20 minutes. Over a denominator of 12:

of the job per hour. Inverting gives $\frac{4}{3}$ hours, which is 1 hour 20 minutes.

• A: This is 3/4 of an hour, the combined rate, used as the time without inverting.
• B: Adding the three times makes the team slower than any single scanner.
• C: This is the average of the three times, which is longer than the fastest scanner alone.
• D (correct): The combined rate is 3/4 of the job per hour, so the time is 4/3 hours, or 1 hour 20 minutes.

Answer: D

Correct answer: 24 hours. Subtract the known rate from the team rate:

The other technician alone needs 24 hours.

• A: Adding the rates instead of subtracting combines the team with one of its own members.
• B: Adding the times does not separate the unknown worker's rate from the team rate.
• C: Subtracting the times gives a worker faster than the whole team, which is impossible.
• D (correct): The missing rate is 1/8 minus 1/12, which is 1/24, so the job takes 24 hours alone.

Answer: B

Correct answer: 15 hours. The crew paints

classroom per hour. For 10 classrooms:

• A: Multiplying 10 by the rate of 2/3 room per hour gives a number with the wrong meaning; time is rooms divided by rate.
• B (correct): At 2/3 classroom per hour, 10 classrooms take 10 divided by 2/3, or 15 hours.
• C: Multiplying 10 rooms by 6 hours treats 6 hours as the time for each single room.
• D: Simply doubling the time fits 8 rooms, but 10 rooms is 2.5 times the original job.

Answer: D

Correct answer: 4 hours. In 3 hours the welder finishes

leaving $\frac{2}{3}$. Together they do

per hour.

• A: This is how long the coworker alone would need for the remaining two-thirds, leaving out the welder's help.
• B: This is the total elapsed time including her first 3 hours, but the question asks for time after the coworker joins.
• C: This is the time for the whole job together, ignoring the third already finished.
• D (correct): Two-thirds of the job remains, and at 1/6 per hour that takes 4 hours.

Answer: D

Correct answer: 30 minutes. The net gain is

per minute. The hopper needs

more pounds, so the time is

• A: Dividing the full 1,200 pounds by 30 forgets the 300 pounds already in the hopper.
• B: Adding the inflow and outflow treats the outflow as helping to fill the hopper.
• C: Using only the 90-pound inflow ignores the grain flowing out the bottom.
• D (correct): The hopper gains 30 pounds per minute and needs 900 more pounds, which takes 30 minutes.

Answer: B

Correct answer: 8 hours. Together they do

per hour, so in 2 hours they finish $\frac{1}{2}$. The slower cleaner needs

for the other half. Total:

• A: This has the faster cleaner finishing the second half, but the faster one is the one who left.
• B (correct): Half the job is done in the first 2 hours, and the slower cleaner needs 6 more hours for the remaining half.
• C: This is only the slower cleaner's solo time for the last half; the first 2 hours must be added.
• D: This assumes both cleaners stay for the whole job.

Answer: C

Correct answer: 6 hours. After 2 hours, $\frac{2}{5}$ of the tank is full and $\frac{3}{5}$ remains. With the drain open the net rate is

tank per hour.

• A: Adding the drain's rate to the inlet's treats the drain as if it were filling the tank.
• B: This includes the first 2 hours, but the question asks how many more hours are needed.
• C (correct): The remaining 3/5 of the tank fills at a net 1/10 tank per hour, which takes 6 hours.
• D: This is the time for the remaining 3/5 with the inlet alone, ignoring the open drain.

Answer: A

Correct answer: 12 hours. Subtract both known rates from the team rate:

The third worker alone needs 12 hours.

• A (correct): The third worker's rate is 1/2 minus 1/6 minus 1/4, which is 1/12, so the job takes 12 hours alone.
• B: Subtracting times (6 + 4 − 2) does not work; rates must be subtracted, not hours.
• C: Subtracting only the first worker's rate leaves out the second worker's share.
• D: Adding all the rates instead of subtracting gives a worker faster than the whole team.

Answer: A

Correct answer: 25 minutes. Printer A prints 60 pages per minute and Printer B prints 50, so together they print 110 per minute. In the first 5 minutes A prints 300 pages, leaving 2,200. Those take

so the order takes

• A (correct): Printer A prints 300 pages alone in 5 minutes, and the remaining 2,200 pages take 20 minutes at 110 pages per minute.
• B: This is only the time after Printer B starts; the first 5 minutes must be added.
• C: Dividing 2,500 by 110 assumes both printers ran from the start.
• D: Dividing 2,500 by 60 has Printer A doing the whole order alone.

Answer: D

Correct answer: 10.5 hours. Together the rate is

per hour, so in 3 hours they finish $\frac{1}{2}$ of the job.

The slower roofer does $\frac{1}{15}$ per hour, so the remaining half takes

Total:

• A: This is the time if both roofers stayed for the entire job; it ignores that the faster one left.
• B: This is only the time the slower roofer works alone after the other leaves; the first 3 hours must be added.
• C: This assumes the faster roofer stayed to finish the second half, but it was the slower roofer who finished.
• D (correct): Together they finish 1/2 in 3 hours; the slower roofer needs 7.5 more hours for the other half, so 3 + 7.5 = 10.5 hours.

Answer: C

Correct answer: 14 hours. Alone for 5 hours she finishes

leaving $\frac{3}{4}$.

Team rate:

per hour, so the rest takes

Total:

• A: This is only the time after the coworker joins; the question asks for total elapsed time, so the first 5 hours must be added.
• B: This is how long the two would need for the entire job if they started together, ignoring the solo stage.
• C (correct): She finishes 1/4 alone, the pair then needs 9 hours for the remaining 3/4, and 5 + 9 = 14 hours.
• D: This adds the solo 5 hours to a full 12-hour team job, forgetting that 1/4 of the work was already done.

Answer: B

Correct answer: 4 hours 40 minutes. Add the rates over a common denominator:

of the job per hour.

Invert to get the time:

which is 4 hours 40 minutes.

• A: This is half of the faster deckhand's time, which would only be true if both worked as fast as the faster one.
• B (correct): The combined rate is 3/14 of the job per hour, so the time is 14/3 hours, which is 4 hours 40 minutes.
• C: This averages the two times; a team is always faster than either worker alone.
• D: This adds the two times instead of adding the rates.

Answer: D

Correct answer: 7.5 hours. The unknown rate is the team rate minus the known rate:

Invert:

• A: This subtracts the times (5 - 3) instead of the rates.
• B: This adds the two times, which has no meaning for work rates.
• C: This adds the rates instead of subtracting the known worker's rate from the team rate.
• D (correct): Subtracting rates gives 1/3 - 1/5 = 2/15 of the trailer per hour, so the other operator alone needs 15/2 = 7.5 hours.

Answer: D

Correct answer: 1/6. A worker who needs h hours for a job completes $\frac{1}{h}$ of it each hour. Here h = 6, so she completes $\frac{1}{6}$ of the transcript per hour.

• A: This is the number of hours for the whole job, not the fraction finished per hour.
• B: This is the fraction still left after the first hour, not the fraction done each hour.
• C: This halves the correct rate for no reason, as if the job took 12 hours.
• D (correct): A job that takes 6 hours alone is done at a rate of 1 divided by 6, or 1/6 of the job per hour.

Answer: A

Correct answer: 5 hours. Use a common denominator of 30. Inlets add, the drain subtracts:

The tower fills at 1/5 per hour, so it takes 5 hours.

• A (correct): Net rate is 1/6 + 1/10 - 1/15 = 1/5 of the tower per hour, so filling takes 5 hours.
• B: This adds the drain's rate as if it were a third inlet; a drain's rate must be subtracted.
• C: This is the time for the two inlets with the drain closed; it ignores the drain.
• D: This treats the net rate of 1/5 tower per hour as the time, forgetting to invert it.

Answer: D

Correct answer: 30 minutes. The net growth rate is arrivals minus removals:

people per minute.

Time = amount / rate =

• A: This adds the two rates (95 per minute) even though loading removes people from the line.
• B: This uses only the arrival rate of 55 per minute and ignores the people being loaded.
• C: This divides 450 by the loading rate of 40, which does not measure how fast the line grows.
• D (correct): The line grows by 55 - 40 = 15 people per minute, and 450 / 15 = 30 minutes.

Answer: B

Correct answer: 20 minutes. Find each rate:

bottles per minute and

bottles per minute.

Combined:

per minute. Time:

• A: This averages the two rates (95 per minute) instead of adding them.
• B (correct): A fills 120 per minute and B fills 70 per minute, so together 190 per minute, and 3,800 / 190 = 20 minutes.
• C: This uses machine A's rate of 120 per minute alone and leaves out machine B.
• D: This uses machine B's rate of 70 per minute alone and leaves out machine A.

Answer: D

Correct answer: 18 hours. Here one job means one roof. Crew A works at $\frac{2}{9}$ roof per hour and crew B at $\frac{3}{9}$, so together $\frac{5}{9}$ roof per hour.

Time = work / rate:

• A: This multiplies 10 roofs by the rate of 5/9 roof per hour instead of dividing by it.
• B: This is crew B's time working alone; crew A's help is left out.
• C: This averages the two crews' solo times (45 and 30 hours) instead of adding their rates.
• D (correct): Together the crews shingle 5 roofs every 9 hours, or 5/9 roof per hour, so 10 roofs take 10 / (5/9) = 18 hours.

Answer: D

Correct answer: 4 hours. With a common denominator of 24, the three rates are

per hour, so in 2 hours they finish $\frac{1}{2}$.

The two slower pumps drain

per hour, so the remaining half takes

• A: This is the total time for the whole job; the question asks only for the time after the breakdown.
• B: This assumes the pumps keep working at the full three-pump rate after the fastest one stops.
• C: This is how long the two remaining pumps would need for the entire job, ignoring the half already done.
• D (correct): All three drain 1/4 per hour, so 1/2 is done after 2 hours; the remaining two drain 1/8 per hour, so the last half takes 4 hours.

Answer: B

Correct answer: 2/5. Work = rate x time. The rate is $\frac{1}{10}$ of the road per day, so in 4 days the crew finishes

of the road.

• A: This is the fraction still left to regrade, not the fraction already done.
• B (correct): The crew does 1/10 per day, and 4 days times 1/10 equals 4/10, which simplifies to 2/5.
• C: This is the fraction done in one day, not in 4 days.
• D: This inverts the number of days worked instead of multiplying the rate by the time.

Answer: A

Correct answer: 6 hours 40 minutes. The combined rate is the inlet rate minus the drain rate, so the drain rate is the difference:

Invert: $\frac{20}{3}$ hours = 6 hours 40 minutes.

• A (correct): The drain's rate is 1/4 - 1/10 = 3/20 trough per hour, so it empties the trough in 20/3 hours, or 6 hours 40 minutes.
• B: This subtracts the times (10 - 4) instead of subtracting the rates.
• C: This adds the inlet and combined rates instead of subtracting to find what the drain removes.
• D: This adds the two times, which does not give any rate in the problem.

Answer: C

Correct answer: 8.4 days. Pick a job size both times divide evenly: the LCM of 14 and 21 is 42 units.

The crews clear

units per day, so 5 units per day together. Time:

• A: This is half of the faster crew's time, which would require both crews to work as fast as the faster one.
• B: This averages the two times; working together must be faster than either crew alone.
• C (correct): Calling the job 42 units, the crews clear 3 and 2 units per day, so 5 together, and 42 / 5 = 8.4 days.
• D: This adds the times instead of adding the rates.

Answer: A

Correct answer: 1.5 hours. Add the rates:

of the load per hour.

Invert to get the time:

• A (correct): Together they sort 1/2 + 1/6 = 2/3 of the load per hour, so the time is 3/2 = 1.5 hours.
• B: This averages the two times; together they must beat the faster clerk's 2 hours.
• C: This adds the two times instead of adding the rates.
• D: This stops at the combined rate of 2/3 load per hour and forgets to invert it.

Answer: A

Correct answer: 5 hours. Time = work / rate. The whole job is 1, so the time is

• A (correct): A rate of 1/5 of the job per hour means the whole job takes 1 divided by 1/5, or 5 hours.
• B: This treats the rate of 1/5 as 1/5 of an hour; the rate must be inverted to find the time.
• C: This halves the correct time, as if the team rate were 2/5 per hour.
• D: This counts only the 4/5 of the job left after the first hour.

Answer: B

Correct answer: 3 hours. Rewrite each rate with denominator 18:

The tractors plow 1/3 of the field per hour, so they need 3 hours.

• A: This divides the fastest time by 3, which would require all three tractors to be as fast as the fastest one.
• B (correct): Over a common denominator of 18 the rates add to 6/18 = 1/3 of the field per hour, so the job takes 3 hours.
• C: This averages the three times; the team must be faster than any single tractor.
• D: This adds the three times instead of adding the three rates.

Answer: B

Correct answer: 3 hours 20 minutes. In 6 hours the mason finishes

leaving $\frac{5}{8}$.

Team rate:

per hour. Time:

which is 3 hours 20 minutes.

• A: This is the total elapsed time including the mason's first 6 hours; the question asks only for the time after the partner joins.
• B (correct): After 6 hours 5/8 remains; together they lay 3/16 per hour, and 5/8 divided by 3/16 is 10/3 hours, or 3 hours 20 minutes.
• C: This is the time for the pair to lay the entire patio, ignoring the 3/8 already finished.
• D: This lets the partner finish the remaining 5/8 alone and leaves out the mason's continued work.

Answer: C

Correct answer: 25 minutes. When output is counted in items, add the rates directly:

rolls per minute.

Time =

• A: This uses only the first line's rate of 48 rolls per minute.
• B: This uses only the second line's rate of 32 rolls per minute.
• C (correct): Together the lines make 48 + 32 = 80 rolls per minute, and 2,000 / 80 = 25 minutes.
• D: This subtracts the rates (48 - 32 = 16) even though both lines are adding rolls.

Answer: A

Correct answer: 16 hours. Find the rate for one unit of work: 1.5 miles / 6 hours = 0.25 mile per hour.

Then time = work / rate =

• A (correct): The rate is 1.5 / 6 = 0.25 mile per hour, so 4 miles take 4 / 0.25 = 16 hours.
• B: This multiplies 4 miles by the rate of 0.25 mile per hour instead of dividing by it.
• C: This adds the extra 2.5 miles to the 6 hours as if each mile took 1 hour.
• D: This multiplies 4 by 6, treating the original job as 1 mile instead of 1.5 miles.

Answer: C

Correct answer: 12 hours. The pump adds and the leak subtracts:

The tank gains 1/12 per hour, so it fills in 12 hours.

• A: This adds the leak's rate to the pump's rate; a drain's rate must be subtracted.
• B: This subtracts the times (24 - 8) instead of the rates.
• C (correct): The net rate is 1/8 - 1/24 = 2/24 = 1/12 tank per hour, so the tank fills in 12 hours.
• D: This adds the two times, which has no meaning for rates.

Answer: C

Correct answer: 5 hours. Add the rates:

of the container per hour. Invert: 5 hours.

• A: This adds the two times; a second worker shortens the job instead of lengthening it.
• B: This averages the two equal times, which ignores the extra help.
• C (correct): Each forklift does 1/10 per hour, so together they do 2/10 = 1/5 per hour and need 5 hours.
• D: This stops at the combined rate of 1/5 container per hour and forgets to invert it.

Answer: B

Correct answer: 2 hours. Work done by the first inspector:

so $\frac{2}{5}$ remains.

The second inspector's rate is $\frac{1}{5}$ per hour, so she needs

• A: This finishes the remaining 2/5 at the first inspector's slower rate of 1/10 per hour.
• B (correct): The first inspector finishes 6/10 = 3/5, leaving 2/5; at 1/5 per hour the second inspector needs 2 hours.
• C: This divides the 3/5 already finished by the second inspector's rate instead of the 2/5 that remains.
• D: This has both inspectors working together on the rest, but the first one was reassigned.

Answer: A

Correct answer: About 5.1 days. Estimate first: the answer must be less than 9 days and more than half of 9, or 4.5 days.

Exactly:

per day, so the time is

• A (correct): The combined rate is 7/36 of the job per day, so the time is 36/7, which is about 5.1 days and lies between 4.5 and 9 days as it must.
• B: This is less than half of the faster carpenter's 9 days, which is impossible because the partner is slower.
• C: This averages the two times, but working together must be faster than either person alone.
• D: This adds the two times instead of adding the rates.

Answer: B

Correct answer: 15 hours. Time = work / rate. The rate is $\frac{1}{20}$ of the deck per hour, so

• A: This is the time for the remaining 1/4 of the deck, not for 3/4 of it.
• B (correct): At 1/20 of the deck per hour, 3/4 of the deck takes 3/4 divided by 1/20, or 15 hours.
• C: This divides 20 by 3/4, which gives more time for less than the whole deck.
• D: This divides 20 by 1/4, mixing up the part of the deck with the part left over.

Answer: A

Correct answer: 6 hours. Find the unknown rate by subtraction:

brackets per hour for press B.

Time =

• A (correct): Press B makes 900 - 520 = 380 brackets per hour, and 2,280 / 380 = 6 hours.
• B: This uses the combined rate of 900 per hour even though press B runs alone.
• C: This uses press A's rate of 520 per hour instead of press B's rate.
• D: This adds 900 and 520 instead of subtracting to find press B's rate.

Answer: B

Correct answer: 2 hours 24 minutes. Add the rates:

of the lot per hour.

Invert:

Convert the decimal: 0.4 x 60 = 24 minutes, so 2 hours 24 minutes.

• A: This reads 2.4 hours as 2 hours 40 minutes; 0.4 hour is 0.4 x 60 = 24 minutes.
• B (correct): The combined rate is 5/12 of the lot per hour, so the time is 12/5 = 2.4 hours, and 0.4 hour is 24 minutes.
• C: This averages the two times; the team must beat the faster driver's 4 hours.
• D: This adds the times instead of adding the rates.

Answer: C

Correct answer: 6 hours. Stage 1:

per hour, so 4 hours finishes $\frac{1}{2}$.

Stage 2:

per hour, so the remaining half takes

Total:

• A: This is only the time after the third volunteer joins; the first 4 hours must be added.
• B: This is the time if all three had worked together from the start.
• C (correct): The first two finish 1/2 in 4 hours; all three pack 1/4 per hour, so the second half takes 2 hours, for 6 hours in all.
• D: This is how long the first two volunteers would need for the whole job without the third.

Answer: C

Correct answer: 15 hours. Net rate:

trough per hour.

Only half the trough remains:

• A: This is the time to fill a completely empty trough; only half the trough still needs water.
• B: This adds the leak's rate to the inlet's rate instead of subtracting it.
• C (correct): The net rate is 1/10 - 1/15 = 1/30 trough per hour, and the remaining 1/2 trough takes 15 hours.
• D: This subtracts the times (15 - 10) instead of the rates.

Answer: A

Correct answer: 4 hours. Opposing rates subtract: net buildup =

per hour.

Time =

• A (correct): The snow depth grows by 3 - 1 = 2 inches per hour, and 8 / 2 = 4 hours.
• B: This adds the melting rate to the snowfall rate instead of subtracting it.
• C: This uses the snowfall rate alone and ignores the melting.
• D: This divides by the melting rate of 1 inch per hour, which does not measure the buildup.

Answer: D

Correct answer: 2.8 hours. Call the job 30 units. A, B and C do 5, 3 and 2 units per hour.

Stage 1: A and B do 8 units per hour, so 16 units in 2 hours, leaving 14 units. Stage 2: B and C do 5 units per hour, so

• A: This is the total elapsed time; the question asks only for the time after C joins.
• B: This is the time if all three worked together on the whole attic from the start.
• C: This lets C finish the remaining 7/15 alone and leaves out B's continued work.
• D (correct): A and B finish 8/15 in 2 hours, leaving 7/15; B and C do 1/6 per hour, so the rest takes 2.8 hours.

Answer: A

Correct answer: 6 hours. First state what one job is: one driveway. Combined rate:

driveway per hour.

For 3 driveways:

• A (correct): Together they seal 1/3 + 1/6 = 1/2 driveway per hour, so 3 driveways take 3 / (1/2) = 6 hours.
• B: This is the time for one driveway; the job here is three driveways.
• C: This averages the two workers' times (4.5 hours) and multiplies by 3 instead of adding rates.
• D: This multiplies 3 driveways by the rate of 1/2 driveway per hour instead of dividing.

Answer: C

Correct answer: 35 days. Unknown rate = team rate - known rate:

The smaller dredge alone needs 35 days.

• A: This subtracts the times (14 - 10) instead of the rates.
• B: This adds the two times, which does not give the missing worker's time.
• C (correct): The smaller dredge's rate is 1/10 - 1/14 = 4/140 = 1/35 per day, so it needs 35 days.
• D: This adds the team rate and the larger dredge's rate instead of subtracting.

Answer: C

Correct answer: 1 hour 12 minutes. Add the rates:

per hour.

Invert:

and 0.2 x 60 = 12 minutes, so 1 hour 12 minutes.

• A: This averages the two times; the pair must be faster than the faster airman.
• B: This adds the two times instead of adding the rates.
• C (correct): Together they do 5/6 of the job per hour, so the time is 6/5 = 1.2 hours, and 0.2 hour is 12 minutes.
• D: This reads 1.2 hours as 1 hour 20 minutes; 0.2 hour is 0.2 x 60 = 12 minutes.

Answer: D

Correct answer: 7 hours 20 minutes. Stage 1:

filled, so $\frac{2}{3}$ remains.

Stage 2 net rate:

per hour, so

= 5 hours 20 minutes.

Total: 2 hours + 5 hours 20 minutes = 7 hours 20 minutes.

• A: This is only the time after inlet B and the drain open; the first 2 hours must be added.
• B: This is the time to fill the whole cistern at the net rate of 1/8, ignoring the 1/3 already filled.
• C: This adds the drain's rate as if it were filling, instead of subtracting it.
• D (correct): Inlet A fills 1/3 in 2 hours; the net rate then is 1/8 per hour, so the remaining 2/3 takes 16/3 hours, giving 7 hours 20 minutes in all.

Answer: B

Correct answer: 2/5. Combined rate:

per hour.

Work done in 4 hours:

Remaining:

• A: This is the fraction already tiled, not the fraction still untiled.
• B (correct): Together they tile 3/20 per hour, so 4 hours covers 3/5 of the floor and 2/5 remains.
• C: This counts only the tile setter's 4/12 and leaves out the helper's work.
• D: This treats the pair as needing 12 + 15 = 27 hours, adding times instead of rates.