Farmer Joe owns a cow, a goat, and a sheep. The animals each eat grass at a constant rate, and the grass grows at a constant rate. And Farmer Joe occasionally lets them eat the grass on a small pasture of his.

• If the cow and the goat graze together, the pasture is bare after 45 days.
• If the cow and the sheep graze together, the pasture is bare after 60 days.
• If the cow grazes alone, the pasture is bare after 90 days.
• If the goat and the sheep graze together, the pasture is bare after 90 days, also.

How long will it take for the pasture to be bare if all three animals graze together?

(In reply to solution by Charlie)

Though I'm not sure if my solution is correct, I'm not sure if I agree with yours yet.  Here's why:

Look at the 3rd and 4th statements.  One cow takes just as long as a goat and sheep together to clear the field.  Doesn't that mean that c = g+s?  But 5/180 doesn't equal 1/90 + 1/180.

Also, g+s=x Doesn’t that mean that the goat and sheep can never clear the field?

Your values for c, g, s, and x work for the first three equations, but not the last. 90(g+s-x) ends up being 0.

I hope I don’t sound like "oh this is wrong, oh that is wrong." I’m just trying to help find where an error occurred so we can find the correct solution.

Edited on October 12, 2004, 2:48 pm

Posted by nikki on 2004-10-12 14:20:16