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Well, Before I Get the Answer....

A cistern can be filled by 4 pipes. One fills it in a day, another in 2 days, the third in 3 days, and the fourth in 4 days. If all are running together, how soon will they fill the cistern?




NOTE: D.M. (Eugene, OR) suggests the answer is "slightly sooner than most people will compute, since there is less time for evaporation and hence less evaporation that needs to be replaced."

Solution:

Source: Nicomachus, 100