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Diophantus or Heron in Greek Anthology (500 A.D.)

I am a brazen lion; my spouts are my two eyes, my mouth, and the flat of my right foot. My right eye fills a jar in two days, my left eye in three, and my foot in four. My mouth is capable of filling it in six hours, tell me how long all four together will fill it?

Solution:

Suggested Solution (Liam Sharninghausen, WWU student)

Four rates: 1/48 jar per hour, 1/72 jar per hour, 1/96 jar per hour, and 1/6 jar per hour.

In one hour, the amount is 1/[(2)(24)] + 1/[(3)(24)] + 1/[(4)(24)] + 4/24

Or, [1/24][1/2 + 1/3 + 1/4 + 4] = [1/24][6/12 + 4/12 + 3/12 +48/12]

Which equals [1/24][61/12] or 4.72 hours.

Source: R. McGinty & J. Van Beynen's "Story Problems--Let's Make Them Just That," SSAM (April 1982)