The question below is from one of the Manhattan GMAT CATS. My question stems from the explanation, which is sort of contradictory to the Manhattan word problem book. The CAT explanation explains the following in one section...


This question can also be solved algebraically.
Since the trains traveled the z miles in x and y hours, their speeds can be represented as z/x and z/y respectively.
It goes on to say the distance can be represented by

zt/x for the high speed training, and zt/y for the regular speed. Total they will go z distance. I completely understand this, but then it says "Since the two distances sum to the total when the two trains meet, we can set up the following equation:
zt/x + zt/y = z. My problem here is that in this example Manhattan added across the RTD matrix, but in the word translations book you would typically create two equations going down the chart.

Why in this case did we create a equation going across the chart? Is it because we do not know the total distance?

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It takes the high-speed train x hours to travel the z miles from Town A to Town B at a constant rate, while it takes the regular train y hours to travel the same distance at a constant rate. If the high-speed train leaves Town A for Town B at the same time that the regular train leaves Town B for Town A, how many more miles will the high-speed train have traveled than the regular train when the two trains pass each other?


z(y – x)
--------
x + y


z(x – y)
--------
x + y


z(x + y)
--------
y – x


xy(x – y)
--------
x + y


xy(y – x)
---------
x + y

you have to work up and down the chart to generate the expressions zt/x and zt/y in the first place. these expressions don't produce themselves; they are the result of applying the equation rt = d to the columns of the table (or rows, if you write rt = d across the table instead of down it).

in just about every rtd problem, you must work across the different columns to generate a relationship between the different entities / people / legs of the journey / whatever else. normally you do so after you fill in the rtd chart vertically (as you did by generating the expressions zt/x and zt/y), but there's little point in an rtd problem if the different rtd's aren't interrelated in some way.
in this particular problem, that interrelationship happens to be (distance 1) + (distance 2) = (total distance).], because the trains are meeting each other coming from opposite directions.