I don't understand how someone can work for a company for two months and still not know how to do their job? Something isn't right about that. Talk to your supervisor. You don't get paid for two jobs, stop stressing yourself.

What's your dismissal policy like?

I'd say after 2 months, it's your own fault for not speaking to your supervisor. Or your coworker is super smart because they get paid for doing nothing while you do everything and after 2 months they know you haven't talked to anyone yet and will continue to act "stupid" because you're letting them get away with it. SPEAK UP, IT'S YOUR OWN FAULT!

Your co-worker isn't George Costanza is he?

my dad got in the same position but it was a new system and the guy wasn't just getting it but then they fire him because he wasn't getting it and couldn't get to a point where he could do him self my dad was bounce back and forth tabs to much and miss important stuff

You're only stuck doing both jobs if you're unwilling to let your boss know he's clearly not working out.

Well, maybe you suck as a tutor? Or maybe the person is just an idiot. If you get in trouble, be sure to mention this to your manager.

OP here. I told my managers after two weeks that the trainee just was not getting it. They told me to give him time to pick it up. Tell higher ups every other day that trainee is not working out and finally told them I would not be helping him anymore. He is sinking fast. Don't think he will be around much longer. I have trained a number of people for this position and they all have had it figured out within a couple of days. I don't think it's my training.

I'm glad to see that you've taken steps to get rid of him.