Question
A tank can be filled by pipe A in 6 hours and by pipe B
in 8 hours. There is also a waste pipe C which can empty the full tank in 12 hours. If all three pipes are opened together when the tank is empty, in how many hours will the tank be filled?Solution
ATQ, Rates of work: A fills 1/6 of tank per hour B fills 1/8 of tank per hour C empties 1/12 of tank per hour Net rate = 1/6 + 1/8 − 1/12 LCM of 6, 8, 12 is 24: 1/6 = 4/24 1/8 = 3/24 1/12 = 2/24 Net = (4 + 3 − 2)/24 = 5/24 of tank per hour Time = 1 ÷ (5/24) = 24/5 = 4.8 hours.
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