> > > > > "If 3 cats can kill 3 rats in 3 minutes, how long will it take 100 cats to kill 100 rats?"
> [Et cetera, et cetera, don't forget to consider lots and lots of variables...]

Well, there's obviously only one real solution. We'll have to do it experimentally. (Anyone got any rats and cats that they don't need or want anymore? Well, if not, we can always model their behavior on a computer instead...)

However, I expect we'll find (given the randomness factor and all that) that the amount of time it would take to kill the rats would vary, even if the individual cats were kept constant (although the rats would have to be switched off, because they would die in every trial). If we plugged our results into a graphing calculator (or similar computer program), it could then use a formula that I don't remember to find standard deviation, which would tell us something if the rat-killing times fell exactly into a bell curve (which I doubt they would, but in math we learn to ignore these sorts of little details...).

Without this data, we'll have to make all kinds of assumptions. So: assuming that the example given (three minutes) is typical, we can perhaps assume that the mean (average) amount of time it takes for a cat to kill a rat is three minutes. The time may vary by quite a bit (I imagine, since different cats and different rats would interact in different ways), but it can't vary by more than three minutes because then it would be theoretically possible for a cat to kill a rat in zero minutes or negative time! Therefore, if we say that the standard deviation is about one-third of the available time (one minute), we can't be too far off. (According to my data sheet, this would mean that 0.13% of the rats would die within about 1 second. However, since there's only 100 rats, this represents 0.13 rats, and this rounds down to zero).

Assuming a standard curve, the data (mean three minutes, standard deviation one minute) can then be normalized by finding the z-scores and a data sheet could be used to find the probability of the rats all being killed within a particular amount of time. Because three minutes was "declared" to be the average, the rats would die in under three minutes fifty percent of the time (on a standard normal curve). Additionally, it can be determined that 84.13% of the time, the rats would die in under four minutes, and 97.72% of the time the rats would die within five minutes. There is almost a 100% probability (99.87%, to be exact) that the cats could declare victory in six minutes.

Going the other way, there is a 15.87% chance that the rats would be eliminated in under two minutes, and a 2.28% chance that they would be eliminated in one minute.

From the data provided, I think that's the best I can do.

[Space "I had my Math 30 final today so that's why I know all this" Bar]