Question
Pipe A fills a tank in 12 hours, pipe B in 18 hours and
pipe C empties it in 36 hours. All three are opened together for 3 hours. Then pipe C is closed. In how much more time will the tank be filled?Solution
A's rate = 1/12 B's rate = 1/18 C's rate = -1/36 Net rate together: 1/12 + 1/18 - 1/36 = 3/36 + 2/36 - 1/36 = 4/36 = 1/9 Work done in 3 hours = 3 x 1/9 = 1/3 Remaining work = 1 - 1/3 = 2/3 Now A and B work together: 1/12 + 1/18 = 3/36 + 2/36 = 5/36 Time required = (2/3) / (5/36) = 2/3 x 36/5 = 24/5 = 4.8 hours
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