# The riddle of the cow, the goat and the goose

Hans, a Dutchman with a goat and a goose, meets Katrina, a milkmaid who pulls a cow. When he sees it, the milkmaid gets scared and screams.

- "What's wrong? Why do you scream? ”Asks Hans.

- "You're going to kiss me against my will," says the milkmaid.

- “How could I do that if I carry these two animals in my hands that keep moving?” Asks Hans.

- "What prevents you from throwing the cane on the ground, tying the goat and putting the goose in my milk bucket?" Asks the girl.

- "Because that cranky cow looks like he is looking forward to nailing my horns," says Hans.

- "Oh no! This cow would not horny anyone. You could also take advantage of putting the three animals to graze in my field! ”Replies the frightened milkmaid.

And here begins the most curious puzzle of how many we have presented. As it turns out, Hans and Katrina get tangled up in a conversation in which they conclude that the goat and the goose would eat the same amount of grass together as the cow. So; if in that field the cow and the goat could graze for 45 days, or the cow and the goose for 60 days, or the goat and the goose for 90 days;

How long would that field supply the cow, the goat and the goose?

Please answer quickly as Hans and Katrina are waiting for the answer to be able to make a little house together
in that field

#### Solution

In this riddle we have to contemplate the daily growth of the grass. We are told that the cow eats the same as the goat and the goose together. Therefore, if the cow and the goat eat the grass of that field plus what will grow in 45 days, two goats and a goose will do the same at the same time. As a goat and a goose will hold for twice as long, we know that the goat will consume the initial grass in 90 days, while the goose will be able to live with the grass that grows in that interval. So, if the cow eats 1/60 of the stock per day, and the goat 1/90, together they would eat 1/36.

So the cow and the goat would eat the available grass in 36 days, while the goose would be in charge of eating what grew each day.