Math Help - Rate/Time/Distance problem

This is one aspect of math that always gets me, I could use some help! This is the problem:

Students are traveling in two cars to a football game 135 miles away. The first car leaves on time and travels at an average speed of 45 miles per hour. The second car starts 1/2 an hour later and travels at an average speed of 55mph. How long will it take for the second car to catch up to the first? Will the second car catch up to the first before the first car arrives at the game?

I've figured that the first car will already be 45/2 (22.5) miles ahead of the second car by the time it starts and that they will meet just after two hours, but is there a way to set up a formula for this problem? Thanks!

Hi shenaniganny

Let the students start at O and meet at A. After half an hour, first student will travel distance d to reach A and second student will travel distance 22.5 + d to reach A. They travel for the same time.

Can you set up two equations using s = vt ?