Let r be the speed of the slower car, in mph


Then the speed of the faster car is (r+9) mph.


The "time equation" is

 -  = 1     ("second car, traveling 9 mph faster than the first car, makes the same trip in 1 h less time")


304*(r+9) - 304r = r*(r+9)

2736 = r^2 + 9r

r^2 + 9r - 2736 = 0

(r-48)*(r+57) = 0


The only positive root is  r= 48 mph.


It is the speed of the slower car.


Answer.  The speed of the slower car is 48 mph;  of the faster car  48+9 = 57 mph.