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?

At first glance the answer appears to be 30, but SK wouldn't rate it a 3 if that was the case. 

After taking a closer look at it, I noticed that the Goat eats twice as fast as the cow.  The sheep eats 1.5 times as fast as the cow. 

If all three eat at the same time it is the same as 4.5 cows eating. 

I know the cow will eat the pasture in 90 days, so I devide 90 by 4.5 and come up with 20 days.

20 days is my guess

Posted by Bruce Brantley on 2004-10-16 07:44:05