Be in Arcade mode and use the sports car. Some luck is 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 hitting 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.