Answer:
The runners are 0.159 mi to the west of the flagpole.
Step-by-step explanation:
Let´s place the origin of the frame of reference at the point where the flagpole is located.
The initial position of runner A is 3.91 mi and his velocity is -6.04 mi/h
The initial position of runner B is -2.95 mi and his velocity is 5.00 mi/h
When both runners meet, their position is the same. The equation of the position of each runner is:
x = x0 + v · t
Where
x = position at time t
x0 = initial position
v = velocity
t = time
Then, at the meeting point:
x runner A = x runner B
3.91 mi - 6.04 mi/h · t = -2.95 mi + 5.00m/h · t
Solving for t:
3.91 mi + 2.95 mi = 5.00m/h · t + 6.04 mi/h · t
6.86 mi = 11.04 mi/h · t
t = 0.621 h
Now, we use this time to find the meeting point. We can use the equation of any runner. Let´s use the position of runner A:
x = 3.91 mi - 6.04 mi/h · 0.621 h = 0.159 mi
Since the position is positive, the runners met 0.159 mi to the west of the flagpole.