Question 1200985
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Here are a couple of quick informal methods for solving the problem, if a formal algebraic solution, as shown by the other tutors, is not required.<br>
It takes the inlet pipe 9 hours to fill the pool, so it takes 4*9 = 36 hours for the drain pipe to empty it.<br>
Consider a time length of 36 hours -- the least common multiple of 9 hours and 36 hours.  In 36 hours the inlet pipe could fill the pool 4 times, while in 36 hours the drain pipe could empty it once.  So in 36 hours with the inlet pipe and drain pipe both open, they could fill the pool 4-1 = 3 times.<br>
But that means the two together could fill the one pool in 36/3 = 12 hours.<br>
And here is another quick path to the solution, using logical reasoning.<br>
Since the drain pipe works 1/4 as fast as the inlet pipe, when both pipes are working the pool gets filled only 3/4 as fast as when the drain pipe is closed.  And since it normally takes the inlet pipe 9 hours to fill the tank, the amount of time it takes the pool to fill when the drain pipe is open is 9/(3/4) = 9*(4/3) = 12 hours.<br>