Greek Anthology Book XIV: Metrodorus: 142

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

• 1918: W.R. Paton: The Greek Anthology Book XIV ... (previous) ... (next): Metrodorus' Arithmetical Epigrams: $142$