# Trains Problem

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1. Sep 14, 2015

### Starsfall

1. The problem statement, all variables and given/known data
Two trains run in opposite directions on parallel tracks. Train A is 30 meters long and runs east to west at 60 mph. Train B is 45 meters long and runs west to east. It takes 0.5 seconds for the trains to pass each other. How fast is train B travelling? What is the velocity of train B relative to train A?

2. Relevant equations

3. The attempt at a solution
I'm new to physics and lost with this problem. The first thing I did was convert mph to m/s. (60 miles/hour x 1609m/1m x 1 hour/3600s). I got 26.82 m/s but I don't know where to go from there?

2. Sep 14, 2015

### Staff: Mentor

Welcome to PF!

I would first try drawing a diagram of the problem and see if you figure it out from there.

You could also assign the other train a velocity of x and think about velocity addition and how it may help you solve it.

Think about what it means for two trains to pass in 0.5 secs as in front to front and end to end.

3. Sep 14, 2015

### Starsfall

I drew a sketch but that didn't seem to help much. I was thinking maybe 26.82 m/s x 0.5s = 13.02 m/s. I'm just really confused.

4. Sep 15, 2015

### haruspex

It will be simplest to work in terms of relative motion. Consider an observer travelling at the rear of train A. The observer considers A to be stationary, so sees B travelling at the combined speed.
The observer sees the front of train B pass the front of train A, then half a second later the rear of train B pass herself. How far does it appear that train B has moved in that time?

5. Sep 15, 2015

### r26h

Would it be 75 meters?

6. Sep 15, 2015

### SammyS

Staff Emeritus
Yes.

7. Sep 15, 2015

### haruspex

Can you now answer the second question, the relative velocity?