I understand this concept after reviewing it thoroughly, but still have some questions that I am hoping someone can clarify. I know that when two things are traveling toward each other I should combine their speed and that when one thing is catching up with something ahead of it, I should subtract the fast-slow and get the "real" speed. However, take a look at the below question from Word Translation question bank:

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.

The answer is A. Statement 1 is sufficient.

(1) SUFFICIENT: This tells us that B started traveling 1 hour after Train A started traveling. From the question we know that Train A had been traveling for 2 hours when the trains passed each other. Thus, train B, which started 1 hour later, must have been traveling for 2 - 1 = 1 hour when the trains passed each other.

Let’s call the point at which the two trains pass each other Point P. Train A travels from Town H to Point P in 2 hours, while Train B travels from Town G to Point P in 1 hour. Adding up these distances and times, we have it that the two trains covered the entire distance between the towns in 3 (i.e. 2 + 1) hours of combined travel time. Since both trains travel at the same rate, it will take 3 hours for either train to cover the entire distance alone. Thus, from Statement (1) we know that it will take Train B 3 hours to travel between Town G and Town H.

My question is: Is 1 sufficient because the trains are going at the same rate? Meaning, 1 would NOT be sufficient had the question not specified that they were going at the same speed?

Thanks.

correct, #1 would not be sufficient if that were the case.
you can prove this to yourself without even plugging any numbers, by considering the following two cases:

* case one: let's say train b is obnoxiously slow, and it meets train a after two hours only because train a is barreling toward it at breakneck speed. in this case, then, the answer to the question is going to be a very, very long time indeed.

* case two: let's say train a is obnoxiously slow, and train b barrels toward train a at breakneck speed and meets train a only a few miles from where train a started. in this case, the answer to the problem will be barely over 1 hour.

therefore, insufficient.