Skip to main content

Challenge 46: Sheepish

Can you work out how long it would take 2 sheep to eat all the grass in my field?

Farmer Giles has an overgrown field and decides to buy a small flock of sheep to eat the grass.

Each sheep eats grass at the same constant rate, and the grass grows at a constant rate.

Giles calculates that 8 sheep would take 10 days to clear the field of all grass, while 6 sheep would take 15 days.

a) How long would it take 2 sheep to clear the field?

b) The field can’t be used for growing crops until it has been completely cleared. For every day it remains unused Giles loses £90 of potential earnings. If a sheep costs £150, how many should Giles buy to minimise his losses?