SOLUTION: To fill a swimming pool requires 4 hours if water enters through an inlet pipe​ alone, or 7 hours if water enters through a hose alone. An outlet pipe can drain the pool in

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Question 1020668: To fill a swimming pool requires 4 hours if water enters through an inlet pipe​ alone, or 7 hours if water enters through a hose alone. An outlet pipe can drain the pool in 9 hours. If the inlet​ pipe, hose, and outlet pipe are all being used​ simultaneously, how long will it take to fill the​ pool?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Reciprocal of the sum of the individual rates. 

PIPE         RATE

inlet        0%2B1%2F4

hose         0%2B1%2F7

outlet        -1%2F9

All pipes working simultaneously, the rate in POOLS per HOUR is 1%2F4%2B1%2F7-1%2F9.

First step is %281%2F4%29%2863%2F63%29%2B%281%2F7%29%2836%2F36%29-%281%2F9%29%2828%2F28%29.

Next step can be %2863%2B36-28%29%2F%284%2A7%2A9%29.