Question 292296
Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r

let r=rate of one car
and r+12=rate of the other car
After 4 hours the car travelling faster has travelled 4(r+12)mi
After 4.5 hours the car travelling slower has travelled 4.5r mi
Now we are told that the difference between these distances is 24 mi, so:

4(r+12)-4.5r=24
4r+48-4.5r=24 subtract 48 from each side
4r-4.5r=24-48
-0.5r=-24
r=48 mph----------------rate of slower car
r+12=48+12=60 mph---rate of faster car
CK
48*4.5=216 mi
60*4=240 mi
240-216=24 mi

hope this helps--ptaylor