Cars A and B are racing each other along the same straight road in the following manner: Car A has a head start and is a distance Da beyond the starting line at t=0. The starting line is at x=0. Car A travels at a constant speed Va. Car B starts at the starting line but has a better engine than Car A, and thus Car B travels at a constant speed Vb, which is greater than Va.

Question

A. How long after Car B started the race will Car B catch up with Car A?

B. How far from Car B's starting line will the cars be when Car B passes Car A?

Answer 1

When car B catches up, its' distance
traveled will be greater than car A by
an amount equal to Da; but their time
on the road will be equal.

A. da = Va*t = distance car A traveled.

Da + da = Vb*t = distance traveled by car B,

t = (Da + da) / Vb.

B. Da + da = distance from car B start-
ing line.

Answer 2

78