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

Problem
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.

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.