Question

Working togethertwo pumps can drain a certain pool in 6 hours. If it takes the older pump 15 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?

Answer 1

It takes 10 hours for the new pump to drain the pool.

Explanation:

The older pump does the job in 15 hours.

In 1 hours, the older pump does 1/15 of the job.

The newer pump does the job in x hours.

In 1 hours, the newer pump does 1/x of the job.

Working together, in 1 hours the older pump and the newer pump do the following fraction of the job:

1/15 + 1/x = x/15x + 15/15x = (x + 15)/(15x)

The two pumps working together do the job in 6 hours.

In 1 hour, the two pumps do 1/6 of the job.

(x + 15)/(15x) = 1/6

15x = 6(x + 15)

15x = 6x + 90

9x = 90

x = 10

It takes 10 hours for the new pump to drain the pool.