# It takes 10 hours to fill a pool with water, and 20 hours to drain it. If the pool is empty and the drain is open, how long would it take to fill the pool?

May 2, 2018

It will take $20$ hours to fill.

#### Explanation:

If it takes $10$ hours to fill a fool, it means that after $1$ hour, the pool would be $\frac{1}{10}$ full.

If it takes $20$ hours to empty the pool, it means that after $1$ hour, the pool has dropped by $\frac{1}{20}$.

If the pool is filling and draining at the same time, then it will only fill by the difference in these amounts.

After $1$ hour: $\frac{1}{10} - \frac{1}{20}$ is what has filled up.

$\frac{2}{20} - \frac{1}{20} = \frac{1}{20}$

So after $1$ hour we have managed to fill $\frac{1}{20}$ of the pool.

It will therefore take $20$ hours to fill.