Make sure you are in Arcade mode and are using the sports car. Some luck is 
also required. You must pick up a decent amount of boost, at least four or 
five per lap, and use them in the following key areas. At the first hill at 
start of the race, if you get boost from the first pickup, use it. Use a 
second one at the loop de loop. Use the third on the left turn after the loop. 
Save the fourth for the big hill just before you hit the patch of ice. If you 
have enough remaining, use one just before the final jump in the track, the 
area by the candles. Finally, use one as soon as you land that jump. If you are 
not besting 40 seconds on your first lap just restart.