how long will it take for two trains to meet

Question

Train A departed from City A at a speed of 80 kilometers an hour, and at the same time Train B departed from City B. Train B is 50% faster than Train A. The distance between the cities is 600 kilometeres. How long after their departure did the two trains meet?

Answer 1

Assuming that Train A starts at t=0 at the origin and that it is traveling in the positive x direction, Its coordinate (call it xA) at time t is xA = 80t, where t is in hours and xA is in kilometers.

Train B has a speed 50% greater than train A, so its speed is 80 times 1.5= 120km/hour

In this coordinate system, train B is traveling in the negative direction, and it starts out, at t=0, at 600. Its coordinate is xB=600-120t.

When xA=xB, we have 80t = 600 - 120t, and algebra yields t=3 hours. So the trains meet after 3 hours.