Example 1: Meet problem

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 start at the same time and drive toward each other. How long will it take for the two cars to pass each other? 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 2 cars meet together, 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`
`∆t =d/(v_a +v_b)`
Both cars will meet at
`∆x =(d/(v_a +v_b)) v_a = (v_ad)/(v_a +v_b)`