Question

One pump can drain a pool in 8 minutes. when a second pump is also used, the pool only takes 4 minutes to drain. how long would it take the second pump to drain the pool if it were the only pump in use

Answer 1

8 minutes

Explanation:

The first pump can drain in 8 minutes, therefore:

Rate of the first pump = 1/8

Working together, they can drain the pool in 4 minutes, therefore:

Rate of both pumps = 1/4

Let the time taken by the second pump =t

Rate of the second pump = 1/t.

We then have:

`(1)/(8)+ (1)/(t)=(1)/(4)\\$Collect like terms$\\(1)/(t)=(1)/(4)-(1)/(8)\\(1)/(t)=(2-1)/(8)\\(1)/(t)=(1)/(8)\\$Therefore:\\t = 8 minutes`

It would take the second pump 8 minutes to drain the pool alone.