Answer:
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.