Solving for t max in a 1D problem | Car speed, acceleration and timing involved

[CatherineD]

Homework Statement

The general idea is a regular car moving at constant velocity (v0) is attempting to ram a race car whose wheels are spinning at a stop light. The race car waits until the last moment to push the gas pedal, accelerating at constant acceleration (a).
The time the race car starts to accelerate is t=0

I'm trying to find t max, basically after the race car accelerates, the longest time you have for the car (with Vo) to run into the race car.

Homework Equations

Vf=Vi + a(Tf-Ti)
Sf=Si + Vi(Tf-Ti) + 1/2a(Tf-Ti)^2
Vf^2=Vi^2 + 2a (Sf-Si)

The Attempt at a Solution

I'm having a bit of trouble assigning the knowns and unknowns due to no numbers being given, so I'm not sure how to start it.

 

[learningphysics]

It seems like once the race car has reaches v0, it is impossible for the regular car to ram it. How long does it take for the race car to reach v0?