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A Better Mousetrap (Posted on 2004-01-20) Difficulty: 4 of 5
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?

See The Solution Submitted by DJ    
Rating: 4.1818 (11 votes)

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Some Thoughts 2/3 of an answer | Comment 2 of 12 |
Ryan's answer is based on the assumption that if, as in this case, one cat can kill one rat in 6 minutes, then three cats can kill one rat in 2 minutes. This is because 50 minutes is not evenly divisible by 6 minutes, the killing time for one rat by one cat. After 48 minutes, during which each of Ryan's 12 cats has killed 8 rats, for a total kill up to then of 96 rats, Ryan assumes that the remaining 4 rats can be killed in the remaining two minutes by teaming up 3 cats to each of these rats.

Stefanie, loath to make the assumption that just because one cat can kill one rat in 6 minutes that they can team up with the same efficiency, provides enough cats to get the job done in 48 minutes, leaving 9 of the cats with two minutes of rest each and 4 of the cats with 8 minutes rest (9 x 8 + 4 x 7 = 100).

Tom must have convinced the teacher that the cats would get in each other's way. I can't figure a good mathematical reason for choosing 14, however.
Edited on January 20, 2004, 9:13 am
  Posted by Charlie on 2004-01-20 09:09:16
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