=> Hop into the cart after you start the ride and keep your head down. Maybe it won't see you, if it can see.
Start the ride but hide behind something. The creature might think you're on the ride and follow it and get run over.
Obviously, this is the perfect time to ride a roller coaster-- Silent Hill IS known for its awesome rides, after all! At the very worst, you might see a big monocle-wearing face asking if you've had a nice ride and some animatronic miners that strangely seem to be getting closer and closer whenever you can't see them. Maybe you'll even find weapons or supplies on the ride (a la Donkey Kong Country). There's no way this could go wrong... right?
==> Take a second to regret ever stepping foot in a motherfucking evil amusement park
Quick! Get inside the cart!
==> well, everyone knows roller coasters are never dangerous in these sorts of situations. Hop on in and try to go for a ride. Unlikely that the thing'll follow you there!
=> No lines? Sweet! Ride that shit!