Shannon,
20 cars is too large of a group for this scoring technique. Since each car races only 3 times, there would be a large number of ties -- several cars might come in 1st in all three of their races.
The best approach is to break the 20 cars up into smaller groups. Around 7 per group is best. So maybe 3 groups of 7 + 7 + 6.
After these 3 groups race, pick the 2 best from each group and have a final race with 6 or so.
Chris