Greek Anthology Book XIV: Metrodorus: 135

Arithmetical Epigram of Metrodorus

 * We three Loves stand here pouring out water for the bath, sending streams into the fair-flowing tank.


 * I on the right, from my long-winged feet, fill it full in the sixth part of a day;
 * I on the left, from my jar, fill it in four hours;
 * and I in the middle, from my bow, in just half a day.


 * Tell me in what a short time we should fill it, pouring water from wings, bow and jar all at once.

Solution
First note that the day in this context is taken to be $12$ hours long.

Let $t$ be the number of days it takes to fill the tank.

Let $a, b, c$ be the flow rate in numbers of tanks per day of (respectively) the Loves on the right, the left and the middle.

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

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

We have:

and so:

So the tank will be filled in $\dfrac 1 {11}$ of a day.