Greek Anthology Book XIV: Metrodorus: 142

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Arithmetical Epigram of Metrodorus

Arise, work-women, it is past dawn;
a fifth part of three-eighths of what remains is gone by.


Solution

Let $t$ be the time in hours since dawn.

It is assumed that the day is $12$ hours long.


We have:

\(\ds t\) \(=\) \(\ds \dfrac 1 5 \times \dfrac 3 8 \paren {12 - t}\)
\(\ds \leadsto \ \ \) \(\ds 40 t\) \(=\) \(\ds 36 - 3 t\) multiplying through by $40$ to clear the fractions
\(\ds \leadsto \ \ \) \(\ds 43 t\) \(=\) \(\ds 36\)
\(\ds \leadsto \ \ \) \(\ds t\) \(=\) \(\ds \frac {36} {43}\)


So $\dfrac {36} {43}$ of an hour has passed since dawn.

$\blacksquare$


Source of Name

This entry was named for Metrodorus.


Sources