It takes a month for a horse, two months for a goat and three months for a sheep to eat a cart of hay.

Question

It takes a month for a horse, two months for a goat and three months for a sheep to eat a cart of hay. How many months does it take for a horse, a goat and a sheep to eat a cart of hay together?

Answer 1

We know the answer must be less than one month because the horse alone

eats a cart in a month and it will go quicker with the addition of the goat and sheep.

 

Using units of carts per month, or cpm

Horse = 1cpm

goat = 1/2 cpm

sheep = 1/3 cpm

 

together they can eat  1+1/2+1/3 = 11/6 or 1 5/6 carts per month of hay

 

(11/6 carts/month)(m months) = 1 cart

(11/6)m = 1

m = 6/11 months for the three together to eat a cart of hay

 

If desired the 6/11 can be converted to decimal by doing the division