Working together, two pumps can drain a certain pool in 3 hours. If it takes the older pump 9 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?

Question

Do not do any rounding.

Answer 1

Let the time it takes for the newer pump to drain the pool by itself be x hours.

The rate at which the older pump can drain the pool by itself is 1/9 pool per hour.
The rate at which the two pumps together can drain the pool is 1/3 pool per hour.

So, the rate at which the newer pump can drain the pool by itself is 1/x pool per hour.

Since the two pumps together can drain the pool in 3 hours, we have the equation:
1/9 + 1/x = 1/3

Multiplying through by 9x, we get:
x + 9 = 3x
2x = 9
x = 4.5

Therefore, it will take the newer pump 4.5 hours to drain the pool by itself.