#### Answer

The faster car travels at 30 mph, and the slower car travels at 20 mph.

#### Work Step by Step

Let $x$ mph be the speed of the faster car.
Speed of the slower car = $x - 10$
Since both cars used the same time to travel 90 miles and 60 miles respectively, by $Speed = \frac{Distance}{Time}$, we have
$\frac{90}{x} = \frac{60}{x - 10}$
$90(x - 10) = 60x$
$90x - 900 - 60x = 0$
$30x = 900$
$x = 30$
Therefore, the faster car travels at 30 mph, and the slower car travels at 30 - 10 = 20 mph.