A Hole in One?

A barrel has various holes in it.  The first hole empties the barrel in three days; the second hole empties the full barrel in five days; another hole empties the full barrel in 20 hours; and another hole empties the full barrel in 12 hours.  If all the holes are open together, how long will it take to empty the barrel?

Ma'aseh Hoshev (The Art of Calculation), Levi ben Gerson, 1321

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