Kinematics in 1 dimension - 2 objects interlinked, find time

[googol]

A race driver has made a pit stop to refuel. After refueling, he starts from rest and leaves the pit area with an acceleration whose magnitude is 5.5 m/s^2; after 4.1 seconds he enters the main speedway. At the same instant, another car on the speedway and traveling at a constant velocity of 69.4 m/s overtakes and passes the entering car. The entering car maintains its acceleration. How much time is required for the entering car to catch up with the other car?

Homework Equations

I DO NOT understand how do those type of questions. I had a lot of difficulty with this question and could not come up with the right answer. Along with helping me with this question, are there any specific strategies to go about solving these type of questions??

The Attempt at a Solution

After refueling, car #1
Vi= 0m/s
a= 5.5 m/s^2
t= 4.1 s
vf= ? Vf= vi + at
Vf = 0 + (5.5)(4.1)
vf = 22.55 m/s

____
Other car, car #2
V= 69.4 m/s
t= 4.1 s

deltax = vt + 1/2at^2
deltax = (69.4)(4.1) + 0
deltax = 284.54 m

and from here... I'm completely stuck.
Help, please!

 

[lewando]

It helps to draw a diagram or graph of what is going on. I would recommend a graph showing x vs t of both vehicles for starters.