cats eats rats

these cats are independent with each other, so it takes 100 days for a cat eating a rat.

Work rate: $\frac{100\text{ rats}}{100\text{ cats}\times100\text{ days}}$ . Simplify to $\frac{1}{100}$

Thus: $\frac{1}{100} = \frac{1}{1x}$ and $x = 100$ by proportion or by just looking at it. So $\text{number of days taken} = \boxed{100}$

Trick probem,most people would have gotten an answer of 1 but since 100 cats take 100 days to eat a rat,one cat should take 100 days like all the others