Toyota Repair: Battery wont stay up, alternator belt, alternator output

Question
Hello Mr.Ritter,
I own a 1987 Toyota Corolla,4 cyl.,1.6 with carburator.Milage:187,200.I am having an obvious electrical problem.My new battery won't stay up.
I had my parts store to test the alternator and it was bad so I purchased a new one and had my son to install it.I thought I had it fixed.
But after driving it 6 miles the battery is going down again!I shut it off and try to start it back and it won't start.But the lights are bright,wipers work properly,signals work,ect.
But after I charge the battery back up it will start back up,only to run down again.This is so annoying.
However,I did notice the top bolt on the new alternator is only half in.My son says that is as far he could get it to go--he says the bolt is stripped.Could that be causing the trouble?If not,what else could be wrong?Is it something serious?
Thank you for your assistance.


Answer
Normally I would respond that after replacing the battery and there is still a starting problem, there is a problem with the charging system but since you are telling me that when you are having the starting problem the lights are bright and all electrical accessories are working I don't see how the problem could be the battery.
Something just doesn't sound right here,it is possible that the new alternator was not installed correctly, I don't think the bolt has anything to do with it, make sure all the connections are good to the alternator, the only other thing I can recommend is to have the alternator output checked, if you have a voltmeter connect it across the battery terminals and while the engine is running at idle there should be at least 13.6 volts measured across the  battery terminals, anything less than that means that the alternator ids not charging the battery.  Make sure that the alternator belt is tight.