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?

1 Answer
May 2, 2018

Answer:

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 #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.