Greek Anthology Book XIV: 7. - Problem/Historical Note

Historical Note on Problem $7$, Book $\text {XIV}$ of The Greek Anthology
In 's $1918$ translation of, he gives:


 * The scholia propose several, two of which, by not counting fractions, reach the result of four hours; but the strict sum is $3 \frac {33} {37}$ hours.

The above is correct if it is assumed there are $12$ hours in a day.

It would also need to be assumed that, in order to fulfil the conditions of the statement of the problem, the spouts are turned off at night.

This problem was apparently first presented by in his Metrika.

It was still being taught in classrooms up until the middle of the $20$th Century, and was considered the epitome of "useless" mathematics.

This, as points out in his  of $1992$, is a shame, because the idea behind it is far from useless.

Proof
Assuming a $12$-hour day, the following can be calculated:

and so:

So the jar will be filled in $3 \frac {33} {37}$ hours.