Calculating Time to overtake another Car Suppose that you are in a car and that you observe a car behind you travelling at some speed and also that you know the speed at which your car is travelling. Suppose also that the distance between the cars is known, is it possible to calculate the time at which the car coming behind your car will overtake you?

Nice problem

Let $V_A$ be the speed of your car A & $V_B$ be the speed of the car B behind you.

Since car B is to overtake you hence its speed is taken greater than that of your car i.e. $V_B>V_A$

Now, the relative velocity of car B approaching your car is given as $$V_B-V_A$$

Now, at any moment, let $d$ be the distance between your car A & car B behind you then the time taken by car B to overtake you is $$=\frac{\text{distance between car A & B}}{\text{relative velocity of car B w.r.t. car A}}$$ $$=\frac{d}{V_B-V_A}$$