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?

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Answer 1 · 2018-05-02T18:55:43

It will take $20$ hours to fill.

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

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

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: $1/10 - 1/20$ is what has filled up.

$2/20 -1/20 = 1/20$

So after $1$ hour we have managed to fill $1/20$ of the pool.

It will therefore take $20$ hours to fill.