Oooooo, it's about darn time they decided to hold an official competition.
I've personally been on the r/c scene for the last 5-6 years and have seen some pretty darn crazy creations. The following being two of my toys I've hand built... although the latter has been in the works for 4 years and still isn't done and the former has a little touch up work that needs to be finished such as strengthening the rear suspension and making battery mounts to hang the packs off the side of the chassis to keep the center of gravity down.
http://www.mtsquad.com/phpbb2/viewtopic.php?t=116
http://www.mtsquad.com/phpbb2/viewtopic.php?t=59
Anywho, I can't see a drill motor propelling one of those cars past 111. The brushless motor used in the record holding car would hit RPMs past 60,000 and still have power to spare. Hence why the latest craze on the r/c scene has been brushless motors. Compared to brushed motors they're over twice as powerful, more efficient, and more reliable. However, being a nitro guy myself I always ignore the new electric gadgets.
Without a doubt, if you were to build a speed car, you'd need a on-road racing engine. Considering that the newest ones touch 3-4hp and still managed over 35k, I think they'd have enough power. The problem is taking that power and harnessing it in the most efficient of ways. So, and I almost hate saying this, the best drivetrain would be a belted drivetrain. With kevlar belts, it'd just barely be reliable enough to handle that much power. However, I personally think that a 2 wheel r/c vehicle would be the way to go. If you think about it, it's the most aerodynamic, stable (at high speeds), and efficient chassis design to use considering how little rolling resistane there would be. The only problem would be keeping the bike upright during the run while keeping it in a straight line. Perhaps a gyro to control a set of balance weights and some wires hanging off the side to act as training wheels? Either way, that's my two cents on the subject.