.. Catching the rat

Of course, you do. You would need a bait. Search around.

Get some cheesy puffs from the vending machine.

The next item is something you only get when you have gone forward with the case.

And you did the spiritual quest?

Good. Now, to catch the rat. You need a bait ( Take some cheesy puffs from the vending machine ) and something to catch the rat into. Some kind of cage or similar.

Take the loundry basket from the laundry room. Combine the laundry basket with the cheese puffs, from the vending machine, and catch the rat with it.