2420.11 – Hen and a Half

If a hen and a half lays an egg and a half in a day and a half, how long will it take ten hens to lay ten eggs? (This is a famous old problem.)

Solution

Given: $1 \dfrac{1}{2}$ hens, $1 \dfrac{1}{2}$ days, $1 \dfrac{1}{2}$ eggs.

Doubling the hens but not the time: $3$ hens, $1 \dfrac{1}{2}$ days, $3$ egss.

Therefore: $10$ hens, $1 \dfrac{1}{2}$ days, $10$ eggs.

Each hen lays one egg every $1 \dfrac{1}{2}$ days and the answer is $1 \dfrac{1}{2}$ days.