#### Answer

The speed of the first car is 45 miles per hour.
The speed of the second car is 50 miles per hour.

#### Work Step by Step

Let s represent the speed of the first car.
The speed of the second car is s + 5.
Let's suppose that the first car travels east.
After 6 hours, it has traveled s $\times$ 6 = 6s miles.
Since the cars travel in opposite directions, the second car travels west. After 6 hours, it has traveled (s + 5) $\times$ 6 = 6s + 30 miles.
Because they are 570 miles apart after 6 hours, we can solve the following equation:
6s + 6s + 30 = 570
12s + 30 = 570
12s = 540
Divide both sides by 12.
s = 45
The speed of the first car is 45 miles per hour.
The speed of the second car is 45 + 5 = 50 miles per hour.