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Question 724561: Three pipes fill a pool. Pipe A takes 2 hours to fill the pool, Pipe B takes 3 hours to fill the pool, and Pipe C takes 4 hours to fill. The pool has two leaks in it. Leak D takes 8 hours to drain the pool when filled, and Leak E takes 12 hours to drain the filled pool. Determine how long the empty pool takes to fill
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Three pipes fill a pool. Pipe A takes 2 hours to fill the pool, Pipe B takes 3 hours to fill the pool, and Pipe C takes 4 hours to fill. The pool has two leaks in it. Leak D takes 8 hours to drain the pool when filled, and Leak E takes 12 hours to drain the filled pool. Determine how long the empty pool takes to fill
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Let x = time (hours) it takes to fill
then
x(1/2 + 1/3 + 1/4 - 1/8 - 1/12) = 1
multiply both sides by 24 (common denominator):
x(12 + 8 + 6 - 3 - 2) = 24
x(26 - 5) = 24
x(21) = 24
x = 24/21
x = 1.143
or
x = 1 hour and 9 minutes
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