This works for me but keep in mind I have all level 2 upgrade packages and a unique engine part in my Tiburon.
When you decide you want to take on someone for an outrun race don't start the race right away...
Drive behind him for a minute and DRAFT him... wait until you completely fill up your NOS meter.
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I have had alot of success winning on the highways which at first wasnt the case until i found this little trick/cheat. After you have drafted and filled up your meter, follow the opponent car along the highway until you come to an on/off ramp. Quickly initiate the outrun race then slam into him to force him over into the offramp. Quickly slam on your NOS to get your speed up and before he can turn around to follow you, you're gone like a fart in the wind.
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As for city racing it usually doesnt work so well but there are a few areas where you can use this little nudging technique to your advantage. Just make sure while in the city to have a good feel for taking corners. I've also found that if you have decent enough handling that if you drive into oncoming traffic while your opponent is close behind that sometimes if you dodge a car quick enough your opponent will slam into him.. but not usually.
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