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

Puzzles and Curious Problems by Henry Ernest Dudeney: $164$

Cow, Goat and Goose

A farmer found

that his cow and goat would eat all the grass in a certain field in $45$ days,

that the cow and the goose would eat it in $60$ days,

but that it would take the goat and the goose $90$ days to eat it down.

Now, if he had turned cow, goat and goose into the field together, how long would it have taken them to eat all the grass?

Sir Isaac Newton showed us how to solve a puzzle of this kind with the grass growing all the time;

but, for the sake of greater simplicity, we will assume that the season and conditions were such that the grass was not growing.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $164$. -- Cow, Goat and Goose
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $231$. Cow, Goat and Goose