The Race is the way to get out of Salt City. To access this event you either need to get all the Car Parts to fix Mark's car, or carry out Carla's plan of cutting Stan's brakes.
After you have woken up, go to see Mark in the church. After you have talked, you can go over to the garage right away if you wish.
Go race! Edit
One lap around the track, fastest one wins. Listen to Mark and Stan talk, if you lose you will have to work for free for 3 months for Stan, but if you win you get the keys to Marks car. Then they will flip a coin to see who will go first around the track, and you get to choose Head or Tails.
You do not actually have to do any driving, but you will watch both of the laps and then hear the results. If you chose to cut Stan's brakes, he will crash his car and it will burst into flames, and you will not need to race. However, this will effectively orphan his four children.
Stan will give Mark his keys and when you are ready to leave Salt City, go talk to Mark. You can find him at the church.
Actually you don't have to get all three parts before you can race. You can find Mark in the church and talk him into just start racing. However the car will blow up if it's not all fixed up. If you give up on the race in the beginning, then Mark will die and Carla will blame you.