Two cars started from the same point and traveled on a straight course in opposite directions for exactly two hours, at which time they were 208 miles apart. If one car traveled, on average, 8 mph faster than the other car, what was the average speed of each car for the 2-hour trip?
I understand Distance = Velocity X Time; however, I am stuck on creating the correct formula for this problem, to determine the speeds of the two cars. Step-by-step reasoning would be very helpful! Thank you.
Let $v$ be the average speed of the slowest car. Then the average speed of the other one is $v+8$. After $2$ hours, the first car travaled $2v$ miles and the second one traveled $2\times(v+8)=2v+16$ miles. Since they go in opposite directions, you know that $2v+2v+16=208$. But$$2v+2v+16=208\iff 4v=192\iff v=48.$$Therefore, the average speed of the slowest car is $48$ miles per hour and the average speed of the other car is $56$ miles per hour.