Bunuel wrote:

One pump drains one-half of a pond in 3 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?

A. 1 hour

B. 1.2 hours

C. 3 hours

D. 5 hours

E. 6 hours

We are given that one pump drains one-half of a pond in three hours. Thus, the rate of that pump is (1/2)/3 = 1/6. When the second pump starts helping to empty the remainder of the pond, i.e., half of the pond, we can let x = the time for the second pump to empty the pond alone. Thus, the rate of the second pump = 1/x. We use the formula for work, work = rate x time, to create the following equation:

(1/6)(1/2) + (1/x)(1/2) = 1/2

1/6 + 1/x = 1

Multiplying the entire equation by 6x, we have:

x + 6 = 6x

6 = 5x

1.2 = x

Thus, the second pump could drain the pond in 1.2 hours.

Answer: B

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