Hello.

I want to give my solution. I don't know if it is perfectly right.

We know that

- After traveling for 2 hrs, Train A passes Train B

and we want to answer

- How long does it take Train B to travel the entire distance between both the towns?

First Statement

1) train B started traveling between Town G and Town H 1 hr after train A started traveling between town H and town G

Let's suppose that Train A started at 9:00 am. Then, Train B started at 10:00 am. Therefore, at 11:00 am Train A passes Train B.

Now, since both Trains travel at the same constant rate, then Train B will take 2 hours to arrive in town H. This implies that Train B will arrive in town H at 1:00 pm, therefore Train B will travel the entire distance between both the towns in 3 hours.

This implies that this statement is SUFFICIENT.

Second Statement

2) train B travels at the rate of 150 mph

Here, we don't know anything about the distance between both the towns or the time both Trains started. Therefore, there is not enough information to give an answer.
Hence, this statement is NOT SUFFICIENT.

In conclusion, the correct answer is the option A.

I hope it helps.