Evolution can't account for rats

Evolution says humans and rats have a common ancestor. Rats have had just as long to evolve as humans, but humans are more intelligent than rats. Why aren't rats getting smarter and smarter? Surely a smarter rat has a better chance of surviving.

Rats of lots of babies at once. You can't have lots of babies at once. Therefore, rats > you.

See the logic here. Our niche is intellence. Rats beat us out at a lot of other things.