Understanding Relative Velocity of Runners Moving in Opposite Directions

[samisoccer9]

Homework Statement

James is running west wrt the ground and Billy is running east wrt the ground, but twice as fast as James. How does the relative velocity of James wrt Billy differ if they are running toward each other or away from each other? Explain.
*wrt = with relation to*

Homework Equations

VJG and VBG

The Attempt at a Solution

This is a word problem, I just started an online grade 12 physics class today so I am sort of clueless and quite confused. So I interpreted it like this. Let's say James was 100m/s, therefore Billy is 200m/s. If they run away from each other, so one left/west one right/east then in relation to the ground it would seem as if Billy covered more distance (which would be true?) and if they were running towards each other, then I thought it would be seen as Billy simply again covering more distance by the time James got there. I need help, please and thanks!

 

[Dr. Courtney]

Drawing a picture will help with almost every physics problem.

Rather than assign a number to the velocities, it is better to use symbols, like Vb and Vj for the velocities of james and billy relative to the ground.

Then Vb = -2Vj

Think about why the sign is negative.