Question

One valve drains a pool in 2 hours, and another drains it in 9 hours. How long will it take to drain the pool with both valves open at the same time? Round to the nearest tenth.

Answer 1

In 1 hour, the first drain drains the pool 1/2 of the way.

In 1 hour, the second drain drains the pool 1/9 of the way.

So we want to know how many hours it takes both of them. We let this equal x. In 1 hour, the amount that both drains drain the pool is 1/x of the way.

1/2 + 1/9 = 1/x

11/18 = 1/x

11x = 18

x = 18/11 hours