How Long Does It Take for a Patrol Car to Catch a Speeder?

[kinematics23]

Homework Statement

A speeder traveling at a constant speed of
109 km/h races past a billboard. A patrol car
pursues from rest with constant acceleration
of (8 km/h)/s until it reaches its maximum
speed of 141 km/h, which it maintains until it
catches up with the speeder.
How long does it take the patrol car to
catch the speeder if it starts moving just as
the speeder passes? Answer in units of s.

How far does each car travel? Answer in units
of km.

Homework Equations

Δx = vot + 1/2at^2
Δx = 1/2(vo + v)t

The Attempt at a Solution

This is an online assignment I am doing. I tried substituting values for the equations with the given info and tried to make it so the speeder equation and the car equation is the same so I can solve for the time and i got 27.3 but it came out wrong when I entered the question online. Since I cannot get the first part I can't get the second part either.

 

[Kurdt]

You need to split this into two parts. You need to find the time taken for the police car to accelerate to top speed and the distance the policeman and the criminal travel in that time, and then you need to find out how long it takes to catch him at the constant speed and add the two times together.