Whenever 2 objects are traveling in OPPOSITE directions (toward each other or away from each other), we can always ADD their rates.
Toward:
x-----> <-----x
The SUM of their individual rates is the rate that the distance between them is CLOSING.

Away:
<----x x----->
The SUM of their individual rates is the rate that the distance between them is INCREASING.

So, these 2 trains will collectively travel the entire 750 miles to meet (crash into) each other at the sum of their individual rates, as EconomistGMAT showed.

Another strategy you can easily employ on distance problems: draw a picture!

Let's say X is the train going east, Y is the train going west:

X|------------------------------------------------|Y
0-----------------------------------------------750


After 1 hr, X has traveled 70 mi, and Y has traveled 80 mi. For Y, count backwards from 750:

|-----X------------------------------------Y-------|
0----70--------------------------------670-----750


After 2 hrs:

|---------X------------------------------Y-----------|
0-------140------------------------590----------750


After 3 hrs:

|--------------X--------------------Y----------------|
0----------210------------------510-------------750


After 4 hrs:

|----------------X------------Y------------------|
0--------------280---------430------------750


After 5 hrs:

|----------------------XY------------------------|
0---------------------350--------------------750


The answer is C.

This technique takes a bit longer, but for some people, drawing it out helps to visualize, and you're less likely to make a mistake.