3/4 Basic Motion Question

[AirLandBus]

Hey guys, just started 3/4 physics and have forgotten basically everything from 1/2 motion. I need help with this question:

A car travelling with a constant speed of 80km/hr passes a stationary motorcycle policeman. The policeman sets off in pursuit, accelerating uniformly to 80km/hr in 10 seconds and reaching a constant speed of 100km/hr in a further 5 secs. At what time will the policeman catch up with the car.
 Thanks.

[theshunpo]

First of all, you need a good graph of the situation.
The point at which the policeman catches up is when the distances under the graphs are equal.

In my working out, first i converted the 80 and 100km/hr to m/s and left it as a fraction so I didn't make any rounding errors...
The distance traveled by the car is just (where is the time at which they meet).
The distance traveled by the policeman has three parts, his first acceleration to 80km/hr (the triangle) his second acceleration to 100km/hr (the trapezium) then finally, the constant velocity of 100km/hr after 15 seconds. All I did was, find the distance traveled by the policeman and the car in terms of t and equated them. (The rectangular area for the policeman is where (m/s)
(The graph is clearly not to scale it's just to get an idea of what's going on)
Don't mind my purple pen!

Spoiler

[Kel9901]

A car travelling with a constant speed of 80km/hr passes a stationary motorcycle policeman. The policeman sets off in pursuit, accelerating uniformly to 80km/hr in 10 seconds and reaching a constant speed of 100km/hr in a further 5 secs. At what time will the policeman catch up with the car.
 Thanks.
So for the car:
u=v=80 km/hr=22.2 m/s
In 15 seconds, car travels s=ut=333
For the policeman:
First 10 seconds: u=0, v=22.2, t=10, s=?
s=1/2(u+v)t=111
t=10 to 15: u=22.2, v=100 km/hr=27.8 m/s, t=5, s=?
s=1/2(u+v)t=125
111+125=236 therefore policeman doesn't catch up in 15 seconds
Policeman still needs to catch up 333-236=97 m
Difference between the vehicles' speeds=27.8-22.2=5.6
s=97, v (effectively)=5.6, t=?
s=vt
t=s/v=17.5
15+17.5=32.5 s total