Question

Runner A is initially 4.0 km west of a flagpole and is running with a constant velocity of 7.5 km/h due east. Runner B is initially 2.0 km east of the flagpole and is running with a constant velocity of 5.5 km/h due west. How far are the runners from the flagpole when their paths cross?

Answer 1

Runner A is initially 4.0 km west of a flagpole and is running with a constant velocity of 7.5 km/h due east. Runner B is initially 2.0 km east of the flagpole and is running with a constant velocity of 5.5 km/h due west. How far are the runners from the flagpole when their paths cross?

Solution:

At the start runner A and runner B are 4+2=6 km apart.

Eastbound runner data:

$$distance = x km; rate = 7.5 \frac{km}{h}; time = \frac{d}{r} = \frac{x}{7.5}$$

Westbound runner data:

$$distance = 6 - x; rate = 5.5 \frac{km}{h}; time = \frac{d}{r} = \frac{6 - x}{5.5}$$

time east= time west:

$$\frac{x}{7.5} = \frac{6 - x}{5.5}$$ $$5.5x = 45 - 7.5x$$ $$13x = 45$$

$x = 3.46$ (distance eastbound runner goes)

He will meet the westbound runner 4-3.46=0.54 km west of the flagpole.

Answer: eastbound runner will meet the westbound runner 0.54 km west of the flagpole.