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.
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 stop 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