A community swimming pool has two inlet pipes. One pipe can fill the pool in three hours. The other can fill it in six hours. The pool also has one outlet pipe that can empty the pool in four hours. One day, after cleaning the pool, a maintenance man started filling up the pool using the two inlet pipes. However, he forgot to close the outlet pipe. How long did it take to fill the pool with all three pipes open?

2

Answers

2014-11-27T18:15:57+08:00
-one pipe can fill the pool in three hours
this makes the rate for the pipe to fill the pool,
Rate=1/3
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-the other can fill it for 6 hours
Rate=1/6
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Outlet:
-can empty the pool in 4 hours
Rate = -1/4
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Considering that the 3 pipes work at the same time:
let 't' be the number of hours for the pool to be filled
 \frac{1}{3} t +  \frac{1}{6} t -  \frac{1}{4} t = 1
 \frac{1}{4} t = 1
t = 4hours
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2014-11-29T21:18:58+08:00