a) If they are both travelling at the same speed, and decelerate equally, then they would meet in the middle of the 500m (travel 250m more each). Then you just use the formula :
v2=u2+2as, which can be rearranged to:
a=(v2−u2)/2s.
b) Let's say that the car with the working brakes crashes after x metres, so therefore, the car without brakes crashes after travelling 500-x metres.
So therefore you can say that the following equations are both true:
For car with brakes:
s=(u+v)t/2, u=35, v=0, s=x, which gives
x=35t/2For the car without brakes:
s=(u+v)t/2 , u=35, v=35, s=500-x, which gives
500−x=35t Just solve the two simulataneous equations.
Solving the equations will give you t, which you can use to find x.