A Honda moving at 100km/hr is 80 km behind a Ford moving in the same direction at 60 km/hr. How far does the Honda travel before it catches up with the Ford?

Question

anonymous · Answer

Let us fix an x-axis: in the origin of this axis there is the Honda, at the position of 80 km there is the Ford. The two laws of motion are:
$$x(H)= 100 km/h *t$$
$$x(F)= 60 km/h *t + 80 km$$
the Honda will catch the ford when the position is the same: solve the equation
$$60 km/h *t + 80 km= 100 km/h *t$$
then obtain t=2 h
substitute in x(H) and obtain that the Honda has travelled 50 km before catching the Ford!

stormfire1 · Answer

I'd make this problem a lot simpler and use relative velocities.  The relative velocity between the cars is 100km/h-60km/h = 40km/h.  This is the amount the Honda is gaining on the Ford.  Since the Ford is 80km away, it will take 2 hours at 40km/h.