After finishing the shipyards, I wandered back to the beginning of the mine cart track, and discovered I can pay 20 rupees to race against the clock. Is it worth my time? What can I win?
If you complete the "Heart Stopping!" course in under 1:05:00 (one minute, five seconds), you can win a Piece of Heart.
The "Scary!" track will give you rupees, finish it in under 30:00 (thirty seconds) and you will get a silver rupee (worth 100 rupees).
Here are some tips from this forum:
On the last split of the track (the one where it starts going higher again), take the path on the right, it is significantly faster and if you can do it right can shave like 10 seconds off your time.
When there are jumps, flick the wii remote upwards before you hit the jump so you wont lose as much speed.