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GRE Math: Rates Practice Test
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GRE Math: Rates Practice Test
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1. A hose fills an empty tank with water at a rate of 15 liters/second. At the same time, water drains from the tank at a rate of 10 liters/second. If the tank has a capacity of 200 liters, in how many seconds will the tank be half full?
2. Four machines, working independently at the same constant rate, can fill a production lot in 3 hours. How many of these machines would be needed to fill the lot in 30 minutes?
3. Working at a constant rate, a certain hose can fill a pool in 10 minutes. Working at a different constant rate, another hose can fill the same pool in 15 minutes. If the two hoses work together but independently to fill the pool after it is half full, how many minutes will it take the hoses to fill the pool?
4. Working alone at a constant rate, Machine A can produce 15 widgets in 2 minutes. Working alone at a constant rate, Machine B can produce 20 widgets in 3 minutes. If the two machines start working at the same time, after how many minutes will Machine A have produced 40 more widgets than Machine B?
5. Working together at their respective constant rates, Bob and Sam can mow a lawn in 12 hours. If Bob’s rate is twice Sam’s rate, how many hours would it take Bob, working alone, to mow the lawn?
6. The birthrate of a certain species is approximately 500 organisms per day. The death rate of the species is approximately 300 organisms per day. If the population has 50,000 organisms at the beginning of a certain year, approximately how many organisms will be in the population at the end of the year?
7. Susan takes a 45-mile trip. She travels the first 15 miles in 40 minutes. She travels the remaining 30 miles at double the rate at which she traveled the first 15 miles. What is her average speed for the entire trip in miles per minute?
To determine average speed, use the rate formula: Image
8. Working at a constant rate, a cook can create a batch of pasta in 20 minutes. Another cook, working at a constant rate, can create the same batch of pasta in 10 minutes. If the two cooks work together but independently, how many hours will it take them to create 3 batches of pasta?
9. Boris ran the first 12 miles of a 24-mile race in 1.8 hours. If his rate for the entire race was 6 miles per hour, how many hours did it take him to run the last 12 miles?

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