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Chapter 7: Problem 51

It normally takes 2 hours to fill a swimming pool. The pool has developed a slow leak. If the pool were full, it would take 10 hours for all the water to leak out. If the pool is empty, how long will it take to fill it?

Short Answer

Expert verified
So, it will take 2.5 hours to fill the pool with the leak.

Step by step solution

01

Calculating Rates

Firstly, find the rates of the pool filling and leaking. The rate of filling is 1 pool per 2 hours, so the rate is \( \frac{1}{2} \) pool per hour. The rate of leaking is 1 pool per 10 hours, so the rate is \( \frac{1}{10} \) pool per hour.
02

Define the Effective Fill Rate

Taking into account the leak, the effective fill rate is \( \frac{1}{2} - \frac{1}{10} = \frac{2}{5} \) pools per hour.
03

Calculate the Time to Fill the Pool with the Leak

The time it takes to fill the pool with the leak is the reciprocal of the effective fill rate, which is \( \frac{1}{\frac{2}{5}} = 2.5 \) hours.

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