Question

two cars are 12 miles apart and are approaching each other on a straight road. each car is moving at 60 mi/h relative to the road. how long will it be before the cars pass each other? give your answer in minutes

Answer 1

Let $d = 12 mi$, $v = 60\frac{mi}{h}$.

Let the initial positions of the cars be $x_0$ and $x_0 + d$ respectively, and the first car move in the positive $ox$ direction, while the other car in the negative. Hence, the equations of motion of the cars are $x_1(t) = x_0 + v t$, $x_2(t) = (x_0 + d) - v t$. When they pass each other, $x_1(t) = x_2(t)$, from where $2 vt = d$ and $t = \frac{d}{2 v} \approx 0.1 h = 6 min$.