Toyota Repair: Alternator or battery?, battery terminals, alternator

Question
I have a 1992 corolla and it seems the battery has just died. Or, is it the alternator? How can I tell which it is without first buying a new battery. I can start the car with a jump and even after driving 50 miles, there is no battery power. I have to jump the car again.

Thanks

Answer
You just answered your own question, if the battery is dead after driving for 50 miles the alternator is not charging it, replace the alternator.
Hwew is a little test you can do yourself if you have any doubt about what I just recommended: With the engine running, disconnect one of the battery terminals and wait about one minute or so, if the engine dies the alternator is bad.