Car A's average speed was 10 miles per hour greater than that of car B
Let x = Car B's average speed
So, x + 10 = Car A's average speed

The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance
In other words: (car A's travel time) = (car B's travel time) - 2

time = distance/speed
So, we get: 400/(x + 10)) = 400/x - 2
Multiply both sides of the equation by (x + 10) to get: 400 = 400(x + 10)/x - (x + 10)(2)
Multiply both sides of the equation by x to get: 400x = 400(x + 10) - (x)(x + 10)(2)
Expand: 400x = 400x + 4000 - 2x² - 20x
Subtract 400x from both sides to get: 0 = 4000 - 2x² - 20x
Multiply both sides by -1 to get: 0 = -4000 + 2x² + 20x
Rewrite as follows: 2x² + 20x - 4000 = 0
Divide both sides by 2 to get: x² + 10x - 2000 = 0
Factor: (x + 50)(x - 40) = 0
So, EITHER x = -50 OR x = 40
Since the speed can't be negative, it must be the case that x = 40

Answer: 40

Cheers,
Brent