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

by : Problem $26$

 * De Campo et Cursu Canis ac Fugo Leporis: A Dog Chasing a Hare
 * 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?

Solution
The dog travels $675$ feet.

The hare travels $525$ feet.

Proof
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.