Very simply answered:
a) The Valiant never repaired itself. This happened to me once in a new six-cylinder '70 Ford. A freeze plug blew out on a back country road. I panicked and stuffed a rag down the hole (dumb - blew out straight away), and used a two-quart bottle in the car to keep topping up from a creek that ran near the road:
1) Top radiator up
2) Drive car until all cooling water is pumped out and engine starts to seize
3) Stop, and fill bottle again from creek
4) Rinse, repeat
Fortunately there was a garage a few miles away, the engine was run-in and it wasn't summer.
b) Blind panic. Look where the car ends up after he floors it when the train has passed. He doesn't get away - he ends up on top of a sandbank! Have you ever done anything in panic that you would never have done if you'd sat down quietly and thought about it? Check. If this has never happened, congratulations.
