Cars A and B are racing each other along the same straight road in the following
ID: 2167171 • 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 beyond the starting line at . The starting line is at . Car A travels at a constant speed . Car B starts at the starting line but has a better engine than Car A, and thus Car B travels at a constant speed , which is greater than . 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
v_A_ = VA v_B_ = VB D_A_ = XA So, (VB)(T) = (VA)(T) + XA That means that the distance that B covers in T time must be equal to the distance that A covers in T time plus the "advantage distance". Then, T (VB-VA) = XA You move VA to the other side and factor out T Then time becomes, T = XA / (VB-VA) Now, to find the change in distance you take V = distance / time where v = VB distance = ? time = XA / (VB-VA) You solve for distance, which becomes, distance = (Velocity) * (time) or distance = (XA)(VB) / (VB-VA)