Windshield wipers

I have a 94 Hyundai Elantra, 180,000 miles, with a 1.6-liter twin-cam 4-cylinder engine, but that I doubt has anything to do with the problem but I may be wrong. The problem is when I turn on the windshield wipers they work fine but eventually they work their way up the windshield ie from the lowest postition the drivers side windshield wiper moves up to the middle and eventually when it wipes it goes off the windshield all together but the pasengers' side works fine. What may be the problem?