Solving Head Start Questions for Cars A & B Races

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Car A has a head start of distance D_A and travels at a constant speed v_A, while Car B starts at the starting line and travels faster at speed v_B. To determine when Car B will catch up to Car A, the time can be calculated using the equation D_A + v_A * t = v_B * t, leading to t = D_A / (v_B - v_A). The distance from Car B's starting line when it passes Car A can be found by substituting this time into Car B's distance equation, resulting in the distance being v_B * (D_A / (v_B - v_A)). These calculations provide the necessary solutions to the racing scenario.
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Homework Statement


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.
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?



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The Attempt at a Solution

 
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