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Rats build and live in nests.
Hmmm Depending on how many rats...Cat's would. But if there are loads then you need more cats so that the cats don't get hurt.
you can rap rats on each other but, they would probably die and a dump or/and kind of smart person would do it ;) -Thanks for you question-
10000000 rats
Simply because rats will eat pretty much anything. Many animals can be cannibalistic.
If rats can't find plant items to feed on, yes rats will feed on garbage or even animals. However, the animals that rats feed on would already be dead. Rats are scavengers; this is also why rats carry so many diseases. Only when rats can find no other food sources will they turn to something living.
No, why would music kill rats?
Many soldiers used rats as entertainment; they would place a piece of food on the floor and when the rats came round they would all hit them with their spades.
Rats have many predators, however, the availability of their predators would depend on the rats location. A few well known predators would be cats, some dogs, foxes, owls and hawks.
It would still take 3 minutes according to the setup of the question, assuming there are enough rats to make this work. It takes 1 cat 3 minutes to find a rat, and 3 minutes for 3 cats to each find a rat. So 100 cats would only take 3 minutes to find 100 rats. Time is irrelevant since the only factors changing are the cats and the rats. However, this question assumes too many things that would likely not happen. The question assumes an even density of rats, that the cat's are equally able to catch rats, and that there are enough rats.
2 rats