This sounds like the car chase scene in Secret of the Old Clock
(I think that's the right game--aha, just reread RAL's post, and it is Old Clock
). Anyway, as RAL suggests, I found the best way to beat this was to save just before the chase started, then note down every obstacle that you run into. You may have to go back to your save several times and start again, but you should gradually be able to recognize where the pitfalls are located--each time you'll probably get a little farther in the chase, until you finally go all the way.
It's a pain to have to keep using the "another chance" option, but as far as I could figure out, this is the only reliable way to get to the end of this game...