There's not a lot of peanut butter on the board--but there's quite a lot of feed in the four-foot high plastic or cardboard barrel. Besides, rats are naturally curious, and mice are naturally stupid. Just leave enough empty space that the larger rats can't jump out. Feed's kind of like sand...
To get rid of vermin, Dad used to just park the tractor in the shed, close all the doors and windows, and let it run for a few hours.
Carbon Monoxide. Gotta love it.
The most effective trap I ever built was a plastic feed barrel with a board leaning against it, with a peanut butter trail...
Rats will kill anything if they're hungry enough (un)luckily, coop-raised rats generally are not hungry.
A rat will probably not have a lot of success in the daytime, when the hen will kill on sight, but at night, he might be able to slip under there and make off with a chick. But again, he's...