The following question was asked on a math test:

If 6 cats kill 6 rats in 6 minutes, how many will be needed to kill 100 rats in 50 minutes?

Ryan answered 12, Stefanie said 13, and Tom put down 14 for his answer. After looking at their work, the teacher decided to give all three students credit.

What were the arguments that each student made?

(I have a gnawing feeling about rodent puzzles...)

Ryan: "If 6 cats kill 6 rats in 6 minutes, then 6 cats kill 1 rat per minute. In 50 minutes they kill 50 rats. Double that number, 12, will kill 100 rats in 50 minutes."

Stephanie: "If 6 cats kill 6 rats in 6 minutes, then 1 cat kills 50(1/6) = 8.33 rats in 50 minutes. 100/8.33 = slightly more than 12. So you need at least 13 cats."

Tom reasoned exactly like Stephanie, except that he prudently foresaw the possibility of rodent reproduction during those 50 minutes, and specified one extra cat to counteract it. His total was 14 cats.

Posted by Penny on 2004-01-20 12:25:56