Question

As soon as a traffic light turns green, a car speeds up from rest to 50.0 mi/h with a constant acceleration of 9.90 mi/h·s. In the adjoining bike lane, a cyclist speeds up from rest to 20.0 mi/h with a constant acceleration of 13.5 mi/h·s. Each vehicle maintains a constant velocity after reaching its cruising speed.

(a) For how long is the bicycle ahead of the car?

(b) By what maximum distance does the bicycle lead the car?


I ended up with a quadratic equation but the answer was incorrect, but it was so long to solve that I don't know at what point I would go wrong.