The speed of car `A` is `v_a` and the speed of car `B` is `v_b`. The distance between two cars is `d`. Both cars drive toward same direction. How long will car `A` catch up with car `B`? Let's set the position of car `A` equals 0, than the position of car `B` is `d`. `x_(A_i) = 0` `x_(B_i) = d` Equation: `x_f = x_i + v∆t` Solution: Final position of car `A` after some time `∆t` `x_(A_f) = 0 + v_a ∆t` Final position of car `B` after some time `∆t` `x_(B_f) = d + v_b ∆t` At the moment car `A` catch up with car `B`, both car at the same position. `x_(A_f) =x_(B_f)` `=>` `v_a ∆t = d + v_b ∆t` `v_a ∆t-v_b ∆t =d` `(v_a -v_b) ∆t =d` Both cars will meet at