An inlet pipe on a swimming pool

Question

An inlet pipe on a swimming pool can be used to fill the pool in  hours. The drain pipe can be used to empty the pool in  hours. If the pool is  1/2 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?

Answer 1

There are numbers missing in critical spots of the statement of the problem.

How many hours does it take the inlet pipe to fill the pool?

How many hours does it take the drain pipe to empty the pool?

Judging by the remainder of the problem, the inlet pipe is faster than the drain pipe,

otherwise the pool will be empty not full.

THe inlet pipe can fill the pool in X hours. The drain pipe can empty the pool in D hours. D>X

THe inlet pipe fills 1/X of the pool per hour. The drain pipe empties 1/D of the pool per hour.

since D>x, 1 > x/D ---> 1/x > 1/D

So working together, (1/x - 1/d) of the pool is filled per hour.

Let N be the number of hours need to fill up the pool

N ( 1/x - 1/D) = 1/2 <--- needs to fill up the other half of the pool

N ( D - X) = DX/2 <--- multiplies both sides by DX

N = DX/(2(D-X)) = DX/ (2D-2X)

There is the formula you need to solve your problem.

Note that if D=X then it is division by zero. In that case, the same amount

of water going is shall be the same as the same amount of water escaping

and nothing will get accomplished.