SOLUTION: An inlet pipe on a swimming pool can be used to fill the pool in 12 hours. The drain pipe can be used to empty the pool in 16 hours. If the pool is 23 filled and then the inlet pip

Algebra ->  Rate-of-work-word-problems -> SOLUTION: An inlet pipe on a swimming pool can be used to fill the pool in 12 hours. The drain pipe can be used to empty the pool in 16 hours. If the pool is 23 filled and then the inlet pip      Log On


   

Question 998074: An inlet pipe on a swimming pool can be used to fill the pool in 12 hours. The drain pipe can be used to empty the pool in 16 hours. If the pool is 23 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 ikleyn(52751) About Me  (Show Source):
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An inlet pipe on a swimming pool can be used to fill the pool in 12 hours. The drain pipe can be used to empty the pool in 16 hours. If the pool is highlight%282%2F3%29 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
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The rate of the inlet pipe is  1%2F12  of the pool volume per hour.

The rate of the drain pipe is  1%2F16  of the pool volume per hour.

The net rate  (two pipes work simultaneously)  is  1%2F12 - 1%2F16 = 1%2F%283%2A16%29  of the pool volume per hour.

The equation to determine an unknown time  t  for filling  1%2F3  of the remaining volume of the pool is

1%2F%283%2A16%29.t = 1%2F3.

It gives  t = 16  hours.