Question
Pipe A can fill a tank in 6 hours, pipe B in 8 hours, and pipe C can empty it in 12 hours. All three are opened together for 2 hours, after which pipe C is closed. In how much more time will the tank be filled?
Solution
ATQ, A's rate = 1/6 B's rate = 1/8 C's rate = -1/12 Net rate with all three: 1/6 + 1/8 - 1/12 = 4/24 + 3/24 - 2/24 = 5/24 Work done in 2 hours: 2 x 5/24 = 5/12 Remaining work = 1 - 5/12 = 7/12 Now only A and B work: 1/6 + 1/8 = 4/24 + 3/24 = 7/24 Time for remaining work: (7/12) / (7/24) = 2 hours
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