Step 1 – Reger's car is a Ford. Stone's car is yellow. The Ford isn't yellow. Stone didn't finish first. Reger didn't finish last.

Step 2 – Unger's car and the Audi aren't green. The Audi isn't Unger's car. The speeds are:
Green car + 3 = Audi -and- Audi + 2 = Unger

Step 3 – Quincy's car isn't a Honda or a green car. The Honda isn't green.

Step 4 – The BMW is black. The black BMW finished either first or second. Talbot's car didn't finish third and isn't the black BMW.

Step 5 – Neither the Honda nor the Audi was red.

Step 6 – Talbot’s car is either red or green. The Audi, the Honda, and the BMW can’t be either of these colors, and the Ford was driven by Reger. Therefore, Talbot drove the Chevy.

Step 7 - If Talbot has the green car, then the blue car was 1 mph faster than the Audi and 1 mph slower than Unger. In this case the Audi can't be blue; it must be Stone's yellow car. That puts Unger in first place driving the black BMW. Stone's yellow Audi would be edged out by Reger's red Ford taking third place. That puts Quincy in the Honda, which is not true according to clue 3. Therefore, Talbot must have the red car. By elimination, Reger's Ford must be green.

Step 8 - The finishing order can now be determined. The blue and the black cars clearly finished ahead of Talbot, so he didn't finish first or second. Both the Audi and Unger finished ahead of the green car, so Reger wasn't first or second. Reger and Stone finished together, so Talbot must have been in last place. Unger's speed would bring him in ahead of the blue car, which must be Quincy's Audi.