Greek Anthology Book XIV: Metrodorus: 130

Arithmetical Epigram of Metrodorus

 * Of the four spouts one filled the whole tank in a day,
 * the second in two days,
 * the third in three days,
 * and the fourth in four days.


 * What time will all four take to fill it?

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

Let $a, b, c, d$ be the flow rate in numbers of tanks per day of (respectively) the first, second, third and fourth spouts.

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

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

We have:

and so:

So the tank will be filled in $\dfrac {12} {25}$ of a day.