Train P and Q travel from A to B at 100 mph, and 120 mph respectively.

So I was going through a couple of varied DRT problems, and this one took longer than it should. My question is, how can I approach it differently? Or more efficiently?

Train P and Q travel from A to B at 100 mph, and 120 mph respectively. Train Q stops for 10 minutes at station C, but reaches Station B, 5 Minutes before Train P.

A) 50 km
B) 100 km
C) 120 km
D) 150 km

This is not GMAT Material, so only 4 choices.

So, what I initially tried do was the following

-------|--D----|---R---|---T------|
P--------x-------100---- t-5----
-------|--------|--------|---------|
P--------x-------120---- t+10----
-------|--------|--------|---------|

100t-500 = 120t + 1200

Which is obviously wrong. Then I thought about what I'm actually doing

P's time is five minutes behind T's time after T stops for 10 minutes

P's Time - 5 = Q's Time + 10

P's Time = \(\frac{x}{100}\) and Q's Time = \(\frac{x}{120}\)

So we have:

\(\frac{x}{100}\) = \(\frac{x}{120}\) + \(\frac{15}{60}\)

x=150

So, I suppose I was wondering if anyone has any suggestions on tackling these kind of problems? Or maybe a different approach.

-Thanks