SOLUTION: An inlet pipe on a swimming pool can be used to fill the pool in 32 hours. The drain pipe can be used to empty the pool in 33 hours. If the pool is 2/3 filled and then the inlet pi

Algebra ->  Rate-of-work-word-problems -> SOLUTION: An inlet pipe on a swimming pool can be used to fill the pool in 32 hours. The drain pipe can be used to empty the pool in 33 hours. If the pool is 2/3 filled and then the inlet pi      Log On


   

Question 798501: An inlet pipe on a swimming pool can be used to fill the pool in 32 hours. The drain pipe can be used to empty the pool in 33 hours. If the pool is 2/3 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
The job to be done is "fill the pool". The filling rate is 1%2F32 and the emptying rate is like the opposite of a fill rate, in this problem, -%281%2F33%29.

The rate of fill with both pipes open at the same time is 1%2F32-1%2F33=%2833-32%29%2F%2832%2A33%29 pool per hour. POSITIVE, because this situation FILLS the pool, although very slowly.

The amount of pool to be filled is 1%2F3, because it is already 2/3 filled.
Let h = time in hours to fill this 1/3 of the pool.

highlight%28%28%281%29%2F%2832%2A33%29%29h=1%2F3%29
Find h.