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 re(2): Not sure if this is right, but.... MORE confused now by nikki)

Duh! I forgot that I accounted for the negativity of the grass rate in the matrix, so my rate wouldn’t have the negative sign. Then when I added the rates all together, I forgot that I would have to subtract x since it’s positive.

So my statement "the sum is still P*7/180" is technically true, since P*7/180 = c+g+s+x. But that’s not what I wanted.

I wanted c+g+s – x = 5/180 = 1/36, so one of my solutions finally agrees with Charlie’s! Thank goodness!

The answer is 36 days, and I still prefer my original approach, but without the math mistake =)

Posted by nikki on 2004-10-12 21:03:21