You don't actually race people. It goes on the pending list if they accept your race. Once the race processes at the time it says they will take place, you can either win, lose, or tie.
If you win, you will gain money (if bet) and/or you will gain models (if they have any that wants to leave). If you bet money, you will gain exp from the race. If you race people offline, the race processes immediatly. You cannot race for money while offline though. You cannot race people with less than 50% of your networth if they are offline.