My 71 cutlass started and drove 40 minutes fine, but once I reached my destination and turned off the car later would not start?

No fuel, fuel pump could have gone bad, you could check the fuel pressure it should be around 3 to 6 lbs. Make sure your fuel filter is not plugged, always a good idea to change it out frequently.

I have her In the shop now. I was hoping to avoid spending more money on something that could of possibly been fixed myself.

Hmm... vapor lock? https://en.wikipedia.org/wiki/Vapor_lock

Let us know, we always like to know what it took...

I will inform you guys as soon as I find out,

Ok guys I took my car to the shop but I was shocked to see my car parked face to face ( about 3 f ft ) from the mechanics 71 monte carl both leaking a lrge puddle of trannie fluid. I did have a small leak prior to bringing it there, but now the puddle is very large while strangly his car was doing the same? My question is do you guys thik there was foul play when according to him he had not begun any work yet?..

And btw he said my car started fine when he attempted to start it, and that I probably should of put premium in the tank..