Two Trains Relative Motion [closed]

Question

I am confused about finding the solution to this relative motion problem:

You are on a train traveling east at speed of 20 m/s with respect to the ground. Your friend is sitting on another train traveling west at 28 m/s. As you walk toward the back of your train at 1.4 m/s, what is your velocity with respect to your friend?

My idea is to make the westward velocity negative and the eastward velocity positive. So the car going east is traveling at -28m/s and the car I am on is going +20m/s. Because I am walking towards the back of the train I am also going -1.4m/s. So when I add all these velocities together: -28m/s + 20m/s + -1.4m/s = -9.4m/s. However the problem asks for the velocity in terms of x m/s to the east. My solution is negative (going to the west the way I setup my coordinates).

Could someone please help me understand what I am doing incorrectly and/or show me how to think about this problem?

Answer 1

Your train is travelling east at a speed of 20 m/s, since you walk to the back of your train you are only travellint east at a speed of 18.6 m/s with respect to the ground. Your friend is travelling west at a speed of 28 m/s, or a speed of -28 m/s to the east.

From your friends perspective ground is travelling east at a speed of 28 m/s and you have an additional 18.6 m/s which is 46.6 m/s.

You calculated the sum of the velocities, which would be your speed in respect to the ground if your train were on top of your friends train (or something similar), but the question basically asked for the difference.