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Pipe Schemes

A fountain has 4 receiving pipes, A, B, C, and D; A, B, and C will fill it in 6 hours, B, C, and D in 8 hours, C, D, and A in 10 hours, and D, A, and B in 12 hours; it also has 4 discharging pipes, W, X, Y, and Z; W, X, and Y will empty it in 4 hours, X, Y, and Z in 5 hours, Y, Z, and W in 4 hours, and Z, W, and X in 3 hours. Suppose the pipes are all open and the fountain full, in what time will it be emptied?


Source: Robinson's New Higher Arithmetic, 1895, p. 501