Final answer:
The distance of Runner A from the flagpole when their paths cross is 1.5 km. Since Runner B is running west, the distance of Runner B from the flagpole is also 1.5 km. Therefore, the correct answer is: D. 2.0 km from the flagpole due east
Step-by-step explanation:
Let's analyze the situation:
1. Runner A starts 2.0 km west of the flagpole and runs east at a speed of 2.8 km/h.
2. Runner B starts 4.0 km east of the flagpole and runs west at a speed of 2.0 km/h.
Let t be the time it takes for the runners to meet.
The position of Runner A as a function of time is given by x_A = -2.0 + 2.8t (initial position minus distance covered as he runs to the east).
The position of Runner B as a function of time is given by x_B = 4.0 - 2.0t (initial position plus distance covered as he runs to the west).
To find the time t when the runners meet, set x_A = x_B:
-2.0 + 2.8t = 4.0 - 2.0t
Combine like terms:
4.8t = 6.0
t = 6.0/4.8
t = 1.25
Now, substitute t = 1.25 hours into either x_A or x_B to find the distance from the flagpole:
x_A = -2.0 + 2.8(1.25)
x_A = -2.0 + 3.5
x_A = 1.5 ,km
So, the distance of Runner A from the flagpole when their paths cross is 1.5 km. Since Runner B is running west, the distance of Runner B from the flagpole is also 1.5 km. Therefore, the correct answer is: D. 2.0 km from the flagpole due east