Question 1155701
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Here is an alternative to the method shown by tutor @ikleyn for solving problems like this.  For this particular problem, it makes the solution almost trivial.<br>
Consider the least common multiple of the two given times -- 96 hours and 144 hours.  The least common multiple of those two times is 288 hours.<br>
In 288 hours, the pool could be filled 288/96 = 3 times and it could be drained 288/144 = 2 times.<br>
So in 288 hours with both the fill and drain pipes open the pool could be filled 3-2=1 time.<br>
ANSWER: It takes 288 hours for the pool to fill if both pipes are open.<br>