Henry Ernest Dudeney/Puzzles and Curious Problems/164 - Cow, Goat and Goose/Solution

by : $164$

 * Cow, Goat and Goose

Solution

 * $40$ days.

Proof
Let $t$ be the number of days it takes for them all to eat all the grass.

Let $a, b, c$ be the eating rate in numbers of fields per day of (respectively) cow, goat and goose.

In $t$ days, the various contributions of each of the animals to the eating process is $a t$, $b t$ and $c t$ respectively.

So for the total contribution to be $1$ field, we have:

We have:

and so:

So the field will be eaten bare in $40$ days.