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?

OK, now I've read all the postings.  First, I got the same answer as Charlie, nikki, and Tristan, so I must be right.  Second, I didn't use a calculator, spreadsheet, program, or simultaneous equations.  I just think it is interesting that the same problem can be approached many different ways; sometimes the more complex ways lead to confusion; sometimes a simple method is not powerful enough, but luckily this time it was.

I think I'll coin a term, and call this the mental picture method.  Imagine a mental picture of what is happening in the problem (eg teeth biting through a blade of grass), or a simplified model of the problem.  If you can get your brain around the entire problem all at once, then maybe you are close to having the answer.

Oh, and I didn't use a matrix.  After all, there is no spoon.

Posted by Larry on 2004-10-13 04:14:13