GMAT Quantitative: Rates and Work Practice Questions
Test yourself on Rates and Work with 10 original GMAT practice questions. Pick an answer to see instant feedback and a full explanation.
Free original practice questions for study purposes. Open Exam Prep is an independent study resource and is not affiliated with, endorsed by, or sponsored by the makers of GMAT.
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Answer the questions below — you get instant feedback and a full explanation for each.
1. A machine can produce 240 widgets in 6 hours. At this constant rate, how many widgets can it produce in 9 hours?
Explanation. Rate = 240/6 = 40 widgets/hour. In 9 hours: 40 × 9 = 360 widgets.
2. Pipe A can fill a tank in 4 hours and Pipe B can fill it in 6 hours. Working together, how long will they take to fill the tank?
Explanation. Combined rate = 1/4 + 1/6 = 3/12 + 2/12 = 5/12 tank/hour. Time = 1 ÷ (5/12) = 12/5 = 2.4 hours.
3. Working alone, John completes a job in 5 hours. Working alone, Maria completes the same job in 3 hours. If they work together, what fraction of the job remains after 1 hour?
Explanation. Combined rate = 1/5 + 1/3 = 3/15 + 5/15 = 8/15 per hour. After 1 hour they complete 8/15, so remaining = 1 − 8/15 = 7/15.
4. A car travels from town X to town Y at 60 mph and returns along the same route at 40 mph. What is the average speed for the entire round trip?
Explanation. For equal distances, average speed = harmonic mean = 2(60)(40)/(60+40) = 4800/100 = 48 mph. Note it is NOT the arithmetic mean of 50.
5. 6 workers can build a wall in 10 days. How many days would it take 4 workers to build the same wall, assuming equal work rates?
Explanation. Total work = 6 × 10 = 60 worker-days. With 4 workers: 60/4 = 15 days.
6. Pipe A fills a tank in 3 hours. A drain pipe B empties the full tank in 5 hours. If both are open with an empty tank, how long to fill the tank?
Explanation. Net rate = 1/3 − 1/5 = 5/15 − 3/15 = 2/15 tank/hour. Time = 1 ÷ (2/15) = 15/2 = 7.5 hours.
7. Two trains start at the same time from stations 300 miles apart and travel toward each other. One travels at 50 mph and the other at 70 mph. How long until they meet?
Explanation. Closing speed = 50 + 70 = 120 mph. Time = 300/120 = 2.5 hours.
8. A and B together can finish a task in 8 days. A alone can finish it in 12 days. How long would B alone take?
Explanation. B's rate = 1/8 − 1/12 = 3/24 − 2/24 = 1/24 per day. So B alone takes 24 days.
9. A tank is half full. Pipe A can fill the entire tank in 6 hours and Pipe B can fill it in 4 hours. With both open, how long to fill the remaining half?
Explanation. Combined rate = 1/6 + 1/4 = 2/12 + 3/12 = 5/12 tank/hour. Remaining work = 1/2 tank. Time = (1/2)/(5/12) = (1/2)(12/5) = 6/5 = 1.2 hours.
10. It takes 3 machines 4 hours to produce a batch of parts. To produce the same batch in 3 hours, how many machines are needed (assuming identical rates)?
Explanation. Total work = 3 × 4 = 12 machine-hours. To finish in 3 hours: 12/3 = 4 machines.
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FAQ
What is the core formula for work problems on the GMAT?
Work = Rate × Time. Individual rates add when people or machines work together: combined rate = sum of individual rates. To find total time, take 1 divided by the combined rate (when the job equals 1 unit).
Why can't I just average the two speeds on a round trip?
Because the traveler spends more time at the slower speed, so simple averaging overstates the result. Use total distance ÷ total time, which equals the harmonic mean for equal distances: 2ab/(a+b).
How do I handle a drain or leak in a tank problem?
Treat filling rates as positive and emptying rates as negative. The net rate is the sum (filling − draining). If the net rate is positive the tank fills; if negative, it empties. Then time = 1 ÷ net rate for one full tank.