Greek Anthology Book XIV: Metrodorus: 133

Arithmetical Epigram of Metrodorus

 * What a fine stream do these two river-gods and beautiful Bacchus pour into the bowl.
 * The current of the streams of all is not the same.


 * Nile flowing alone will fill it up in a day, so much water does he spout from his paps,
 * and the thyrsus of Bacchus, sending forth wine, will fill it in three days,
 * and thy horn, Achelous, in two days.


 * Now run all together and you will fill it in a few hours.

Solution
Let $t$ be the number of hours it takes to fill the bowl.

Let $a, b, c$ be the flow rate in numbers of bowls per hour of (respectively) Nile, Bacchus and Achelous.

In $t$ hours, the various contributions of each of the spouts is $a t$, $b t$ and $c t$ respectively.

So for the total contribution to be $1$ bowl, we have:

We have:

and so:

So the bowl will be filled in $\dfrac 6 {11}$ of a day.