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 Not sure if this is right, but.... by nikki)

I notice

S1 + S2 = (c+g) + (c+s) = (P/45 + r) + (P/60 + r)
2c+g+s = P/20 + 2r

But P/45+p/60 = 7P/180

If you then subtract c=P/90+R, you get

c+g+s = P/36 + r

which agrees with my answer (even though my intermediate result is wrong, for the other variables).  Perhaps I had copied something wrong in transcribing my notes to the screen, that gave the wrong values for c,g and s.

Posted by Charlie on 2004-10-12 18:37:44