Runner A is initially 6.0 km west of a flagpole and is running with a constant velocity of 9. km/h due east. Runner B is initially 5.0 km east of the flagpole and is running with a constant velocity of 8.0 km/h due west. How far are the runners from the flagpole when their paths cross?
I did it this way.
time for A to get to the flag pole is t = d/r = 6/9 = 0.667 hour.
time for B to get to the flag pole is t = d/r = 5/8 = 0.625 hour.
That means runner B gets to the flag pole first and will still be running west BEFORE runner A gets to the flag pole. Thus, runner B will run the 5 km + a distance x and runner A will run 6 - x. Setting that up.
Runner A. t = (6-x)/9
Runner B. t = (5+x)/8.
Now set the times equal and solve for x.
(6-x)/9 = (5+x)/8
Their paths will cross at 6 km - x km and 5 km + x km.
x is the distance from the flag pole when their paths cross.
I hope this helps.