Part A.
Given that Initial distance between Car A and Car B is DA, (where Car A is ahead of car B) And
Car A is moving at a constant speed of vA
Car B is moving at a constant speed of vB
Now at the moment when car B catches car A, then
distance traveled by car = distance between car A and Car B + distance traveled by car A
dB = DA + dA
Now we know that distance = Speed*time, Suppose car B catch car A in 'tcatch' time, then in this time
dB = vB*tcatch
dA = vA*tcatch
So,
vB*tcatch = DA + vA*tcatch
tcatch*(vB - vA) = DA
tcatch = DA/(vB - vA)
Part B.
when the car B passes car A, then distance from Car B's starting line will be dB, So from above we know that
dB = vB*tcatch
dB = vB*DA/(vB - vA)
How long after Car B started the race wil Car B catch up with Car A?...
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