Question

Runner A is initially 5.1 km west of a flagpole and is running with a constant velocity of 8.5 km/h due east. Runner B is initially 4.1 km east of the flagpole and is running with a constant velocity of 7.4 km/h due west. How far are the runners from the flagpole when their paths cross? Answer in units of km.

Answer 1

Find the total distance between the two runners:

5.1 + 4.1 = 9.2 km apart.

We want to calculate the distance each runner does:

Runner A distance = X km, rate = 8.5 km/ hr.

Time = X / 8.5

Runner B distance = (9.2 - x) Total distance between the runners minus what runner A runs equals where they meet).

Rate = 7.4 km/hr.

Time = (9.2-x) / 7.4

Now to find where they meet set the two equations equal:

x / 8.5 = (9.2-x) / 7.4

Cross Multiply:

7.4x = 78.2 - 8.5x

Add 8.5x to both sides:

15.9x = 78.2

Divide both sides by 15.9:

x = 78.2 / 15.9

x = 4.918 = 4.9 km.

Since X is the distance runner A runs, subtract that from his distance from the flag pole:

5.1 - 4.9 = 0.2

The runners meet 0.2 km west of the flag pole.