I agree with Rich: testing values works well in this case. Most GMAT experts will consider testing values whenever there are variables in the answer choices.
However, the algebra on this problem isn't too hard to solve. You just have to be careful about the wording in this problem.
The question is asking "
how many miles from home will Aaron jog" - in other words, the
DISTANCE for ONE portion of his journey.
The trick is that the TIME is defined as "a total of t hours jogging and walking." We need to add the times for both portions.
I find that with RATE problems, using a chart helps to stay organized:
Now, fill in the variables given, using "d" for the distance in one direction that we're solving for:
It's clear now the the total time, t, is equal to the sum of the two individual times, d/x and d/y. Create an equation:
Now create a common denominator:
Add the fractions together:
Multiply both sides by xy:
factor out a d:
Divide both sides by (x + y):
The answer is
C.
