I did a youtube search and found it. After a quick look at it, I think that is the one that I'm looking for. I've heard of this movie before, but I just never thought that it might be the right one. Obviously if I'd done more research, I probably should have been able to figure out what the name was. I thank you very much.

You're probably seeking for Catch Me If You Can from 1989.

Hello, my name is Tom. I have been trying to find a movie that I haven't seen in probably 20 years. I'm pretty sure it's about a young guy that street races. I can't remember what kind of car he started with, but he ends up with a '57 Chevy. I remember he has to make a run of 20 miles in 20 minutes. Any help with this would be greatly appreciated. Thank You.