Trains A and B travel at the same constant rate in opposite directions along the same route between Town G and Town H. If, after traveling for 2 hours, Train A passes Train B, how long does it take Train B to travel the entire distance between Town G and Town H?

(1) Train B started traveling between Town G and Town H 1 hour after Train A started traveling between Town H and Town G.

(2) Train B travels at the rate of 150 miles per hour.

I did the following. Using information in the problem and the first statement I made two equations

Train A --> d = r(t + 1)

Train B --> d = rt

rt = rt + r --> t = 1

So --> (t + 1) + t = 1 + 1 + 1 = 3

Since the two trains ultimately traveled the same distance and traveled at the same constant rate, I can treat the two combined trajectories as a single vector in one or the other direction. Therefore, it took train B to travel 3 hours.

Is this correct? Or is my thinking flawed.

Thanks.