electrical question

Hi,
I have an 86 honda accord and a 70 chevy truck and they both run when i jump them and then wont start once i turn them off, even letting them run for like 15 mins.
I used a multi meter today to check them and when they were running the honda had 14.2 volts going to the battery which is right where i want it right? Then about 5 mins later the lights started to dim and i checked it again and it was only getting 6 volts to it. After i shut it off i checked to see what the battery power was at and it was at 10.Its a brand new alternator and battery so i dont know why its doing this and the battery light is on.
As for the truck it was getting 14 volts even. Then i shut it off and it the battery was at 7.9.

So my acual question is are theses alternator problems or battery problems. Both batteries a couple weeks ago when i started messing with these the battery were full charged. I just dont know wehre to start with these now.

thanx
david

The truck has a fried battery.

The accord sounds like a bad alternator. When its getting warm it stops making juice. After you shut it down, how many volts does it show? Often times a bad alternator shows less voltage when running. The fact that its a new alternator makes me suspect it. Its doubtful that its new anyway, most likely rebuilt.

thanx. ya it has to be a rebuilt.the battery read 10 volts.

thanx