Question
A tank can be filled by pipe A in 6 hours and by pipe B
in 8 hours. A waste pipe C 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
A’s rate = 1/6 tank/hour B’s rate = 1/8 tank/hour C’s (waste) rate = −1/12 tank/hour Net rate = 1/6 + 1/8 − 1/12 LCM of 6, 8, 12 = 24 1/6 = 4/24 1/8 = 3/24 1/12 = 2/24 Net = (4 + 3 − 2)/24 = 5/24 tank/hour Time to fill tank = 1 ÷ (5/24) = 24/5 = 4.8 hours = 4 hours 48 minutes.
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