Question

A swimming pool has an input pump for filling the pool and an output pump for emptying the pool. The input pump can fill the pool in 3 hours, and the output pump can drain the pool in 5 hours. As you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. At midnight, you awake to find the pool half empty. Immediately, you turn on the input pump, but you are sleepy and forget to turn off the output pump. At what time will the pool become full?

Answer 1

Answer:

3:45 A.M.

Step-by-step explanation:

The rate at which the output pump drains the pool is:

$D = \frac{1\ pool}{5\ hours}=0.2/hour$

The rate at which the input pump fills the pool is:

$F = \frac{1\ pool}{3\ hours}=0.3333/hour$

If the pump is halfway full, you still need to fill 0.5 of the total volume for it to become full. With both pumps active, the time required is:

$0.5 = (0.3333-0.2)*t\\t=3.75\ h$

If this process started at midnight, after 3.75 hours (3 hours and 45 minutes) it will be 3:45 A.M.