Game of cats and rats

In this problem, we're only accounting for how many minutes the cats can catch all of the rats, not how many rats the cat can catch in one minute. We already know that 5 cats can catch 5 rats in 5 minutes. This must mean that for each cat, one rat is caught within 5 minutes. Therefore, if we have 30 cats and 30 rats, it will still take 5 minutes to catch them all.

If five cats take 5 minutes to catch five rats, then thirty cats take $\text{\_\_\_\_\_}$ minutes to catch thirty rats can be solved as follows

$\frac{x}{30} = \frac{5}{30} \implies x = 5$ , where $x$ is the number of minutes.