A pipe P can fill a tank in 12 hours. Another pipe Q can fill the tank in 18 hours. If pipes P and Q are opened on alternate hours starting with P, then in how many hours will the tank be full?

Taking the least common multiple of 12 and 18 gives an assumed total tank capacity of 36 units. Pipe P fills 3 units per hour and pipe Q fills 2 units per hour; when opened on alternate hours starting with P, they fill 5 units every two hours. After 7 such cycles, lasting 14 hours, 35 units are filled, leaving 1 unit empty. Pipe P is opened for the next hour and fills the remaining 1 unit in 1/3 of an hour. The total time taken is 14 and 1/3 hours, which is exactly 14.33 hours.

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