The problem never specifies how far apart the two towns are so, at first glance, it appears to be impossible to tell how long it takes Train B to travel between the two towns. But the GMAT likes to set traps. Investigate this a little further.
The question stem specifies that the two trains travel at the same constant rate. That's pretty unusual for a GMAT problem...note that down. The problem also doesn't actually say that one starts at one town and the other starts at the other town. It does say that Train A goes for exactly 2 hours before it passes Train B coming in the other direction. (But no info yet on how fast they're going or when or where each one started.)
Finally, it asks how long it would take Train B to travel between the two towns. Since Train A travels at the same rate, it would be enough to know how long it takes either train to travel the full distance between the towns.
Glance at the statements. The first one is much more complicated, so start with statement (2).
(2) INSUFFICIENT: This gives you Train B's rate, so what you really need to find now is the distance between the two towns; if you know that, then you can calculate how long it would take Train B to travel that distance.
Can you determine the distance between Towns G and H?
If Train B travels at 150 miles per hour, so does Train A. The question stem states that Train A runs for 2 hours before it passes Train B, so Train A goes 300 miles before it passes Train B. But when does Train B start? If it starts at the same time as Train A, then it also travels 300 miles before they pass each other...but Train B might have started 3 hours earlier or an hour later. It's not possible to tell.
This statement also doesn't specify that they each start in one of the towns; they could start somewhere in the middle.
(1) SUFFICIENT: This statement is so tricky. First, the statement establishes that Train B starts in Town G and Train A starts in Town H. It also indicates when Train B started relative to Train A: Train B started one hour later. But there's still no information about how far apart the two towns are or how fast the trains are traveling. So how could this possibly be enough?
When the GMAT provides information about relationships in a problem pertaining to rates, be cautious. The information may not seem sufficient at first glance, but could contain an unexpected path to solving.
Consider drawing out what's happening, so you can visualize it. First, Train A starts at Town H and travels alone for an hour towards Town G. Let's say Train A starts at noon.
Then, an hour later at 1pm, Train A keeps going and Train B starts out from Town G towards Town H. They each travel for one hour before they meet (since Train A travels a total of 2 hours before they meet).
Distance-wise, Train A covers the same distance in the second hour as in the first hour, since it's traveling at a constant rate. And here's the key: Train B is traveling at that same rate, too, so it also covers the same distance in one hour that Train A covers in one hour.
When they meet, collectively, they've covered the exact distance between Towns G and H. Train A has traveled for 2 hours and Train B has traveled for 1 hour. And since the trains are traveling at the exact same speed, Train B will continue on its path to Town H, taking the same time that A needed to reach their meeting point: 2 hours. You can essentially think of the three 1-hour increments as representing just one train, traveling at the same speed all the way from Town G to Town H. A train traveling at that exact speed will always take 3 hours to make the trip. In other words, it would take Train B (which is traveling at that speed) exactly 3 hours to make the trip from one town to the other.
The correct answer is (A). Here's an example of one way to sketch out the story (but you can organize things in whatever way works best for your brain!):
