Why didn't Jim escape to Illinois?

I have started reading Huckleberry Finn. I remember starting to read it when I was a boy, having enjoyed Tom Sawyer, but I gave up after a while, because it started to get long and boring. I am enjoying it more now.

Anyway, one of the chapter notes says that Mark Twain was aware that Jim might have escaped to freedom by crossing the river from Missouri to Illinois, but for good reasons decided not to write that plot. I have not got very far into the book, so I don't know how far down the Mississippi they drifted. It makes sense that Jim would not want to cross the bank directly to the Illinois side if he wanted to avoid tracker dogs, but how far down the river did he need to go to shake them off?