Car Collision Problem: Determining Location and Speed at Collision

[Math_Monster]

Homework Statement

A red car with speed 30.0m/s and a blue car with speed 25.0m/s are initially 200m apart and heading toward each other on a one-liner road. The brakes on the red car can produce an acceleration of 3.40m/ss while the breaks on the blue car can produce an acceleration of 3.25m/ss.
A) Do the cars collide? If yes, where?
B) If they collide find speed of each car upon collision.

Homework Equations

I found out both cars' locations if the final velocity is 0, I also found where the time it takes each car to have a velocity of 0. The red car reaches v=0 at 132m and the blue car reaches v=0 at 103.8 m. So clearly they crash because 103.8 < 132. How do I find out WHERE they crash?

The Attempt at a Solution

^

 

[Spinnor]

Write down the distance each car goes as a function of time, X_r and X_b. You also know X_r + X_b = 200 (with a particular choice of coordinates for each car) at t = t_collision.