Propositiones ad Acuendos Juvenes/Problems/26 - De Campo et Cursu Canis ac Fugo Leporis

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $26$

There is a field $150$ feet long.

At one end is a dog, and at the other a hare.

The dog chases when the hare runs.

The dog leaps $9$ feet at a time,

while the hare travels $7$ feet.

How many feet will be travelled by the pursuing dog and the fleeing hare before the hare is seized?

The dog travels $675$ feet.

The hare travels $525$ feet.

Let $x$ be the length of time it takes the dog to catch the hare.

The dog travels $9 x$ during the time the hare travels $7 x$.

Thus we have:

$9 x = 150 + 7 x$

which after algebra gives:

$x = 75$

Hence the result.

$\blacksquare$