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Channeling...to Work Together

There is a reservoir with five channels bringing in water. If only the first channel is open, the reservoir can be filled in 1/3 of a day. The second channel by itself will fill the reservoir in 1 day; the third channel in 2 1/2 days, the fourth one in 3 days, and the fifth one in 5 days. If all the channels are open together, how long will it take to fill the reservoir?

Solution:

Source: Jiuzhang suanshu, China, ca. 200 B.C.