Final answer:
When the paths of Runner A and Runner B cross, Runner A will be 0.12 km east of the flagpole.
Step-by-step explanation:
Distance of Runners from the Flagpole When Paths Cross
To determine the distance of the two runners from the flagpole when their paths cross, we need to calculate the point at which they meet. Let's define east as the positive direction and set up the scenario accordingly:
Runner A is 2.2 km west of the flagpole, which we can consider as -2.2 km.
Runner B is 8.0 km east of the flagpole, or +8.0 km.
Runner A is moving toward the flagpole at 2.0 km/h due east, and Runner B is moving away from the flagpole at 6.8 km/h due west. Since they are moving in opposite directions, we add their speeds to get the speed at which the distance between them is closing:
Combined speed = Speed of A + Speed of B = 2.0 km/h + 6.8 km/h = 8.8 km/h
The initial distance between them is the sum of their distances from the flagpole:
Initial distance = Distance of A from flagpole + Distance of B from flagpole = |-2.2 km| + |8.0 km| = 10.2 km
To find the time at which they will cross paths, we divide the initial distance by their combined speed:
Crossing time = Initial distance / Combined speed = 10.2 km / 8.8 km/h = 1.159 hours
Since Runner A is moving at 2.0 km/h, we can now find the distance they will travel in that time:
Distance traveled by A = Speed of A × Crossing time = 2.0 km/h × 1.159 hours ≈ 2.32 km
Therefore, when their paths cross, Runner A will be 2.32 km east of their starting point. Given that they started 2.2 km west of the flagpole, they will be 0.12 km to the east of the flagpole when they meet Runner B.