Cars A and B are racing each other along the same straight road in the following
ID: 1952078 • Letter: C
Question
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 D(a) beyond the starting line at t=0 . The starting line is at x=0 . Car A travels at a constant speed V(a). Car B starts at the starting line but has a better engine than Car A, and thus Car B travels at a constant speed V(b), which is greater than V(a).How long after Car B started the race will Car B catch up with Car A?
How far from Car B's starting line will the cars be when Car B passes Car A?
Explanation / Answer
distance that car A travels from t=0 x = V(a)t distance that car B travels x + D(a) = V(b)t V(a)t + D(a) = V(b) t t(V(b) - V(a)) = D(a) t = D(a)/(V(b) - V(a)) seconds distance traveled by B beyond t =0 V(b)t = V(b)(D(a))/(V(b)-V(a))