Two pumps are utilized to fill a water tank that is currently empty. The first pump has the capability to fill the tank in 30 hours, while the second pump operates at 3/4 the speed of the first pump. Initially, the first pump works alone for 10 hours, after which the second pump is introduced to finish filling the tank. What is the total time taken to fill the tank?

Answer Choices

Correct answer marked below

11 hours and 30 minutes

12 hours

13 hours and 20 minutes

20 hours and 30 minutes

21 hours and 25 minutes

Correct

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Official Explanation

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We know that the rate of the first pump is 1/30. The second pump, working at 3/4 the speed of the first, has a rate of (1/30) x (3/4) = 3/120 = 1/40. After the first pump operates for 10 hours, it fills 1/30 x 10 = 10/30 = 1/3 of the tank, leaving 2/3 of the tank still to be filled. When the second pump is added, the combined rate becomes 1/30 + 1/40 = 4/120 + 3/120 = 7/120.…

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What this question tests

What it tests

Your ability to combine individual work rates, usually by working with the fraction of a job completed per unit of time.

Common trap

Adding the times instead of the rates, or forgetting to take the reciprocal when combining rates.