# Crossing paths

Runner A is initially 4.54 mi West of a flagpole and is running with a constant velocity of 7.06 mi/h due East. Runner B is initially 4.34 mi East of the flagpole and is running with a constant velocity of 6.82 mi/h due West. Consider East to be in the positive direction. What is the displacement of runner B from the flagpole when their paths cross? Answer in units of mi.

Thanks.

Tom Mattson
Staff Emeritus
Gold Member
Please show how you started, and where you got stuck.

I figured out that it will take A .643hr to reach the flagpole but B .636hr so I know that when the two cross, it's going to be on the left side of the pole, with negative displacement. At .636hrs, A will be 0.05mi away from the pole so they should cross soon. That's where I'm stuck; I think I'm making this too confusing.

Tom Mattson
Staff Emeritus
Gold Member
You should try to write down the displacement of each runner as a function of time, like this:

$$x(t)=vt+x_0$$,

where $x(t)$ is the displacement, $v$ is the velocity, $t$ is the time, and $x_0$ is the initial displacement. To find out when the runners meet, simply equate the two functions and solve for time.

SGT
What is the initial distance between the two runners?
What is their relative velocity?
Dividing the distance by the velocity you find the time they take to cross each other.