Question
A tank has two inlet pipes and one outlet pipe. Pipe A
can fill the tank in 4 hours, and Pipe B can fill it in 6 hours. The outlet pipe C can empty the tank in 8 hours. If all three pipes are opened simultaneously, how much time will it take to fill the tank completely?Solution
Pipe A’s rate = 1/4 tank per hour. Pipe B’s rate = 1/6 tank per hour. Pipe C’s rate = -1/8 tank per hour (negative because it empties the tank). Net rate = (1/4 + 1/6 - 1/8) = (6 + 4 - 3)/24 = 7/24 tank per hour. Time taken to fill the tank = 1 / (7/24) = 24/7 hours ≈ 3.43 hours Correct option: E) None of these
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