Question

Runner A is initially 8.4 km west of a flagpole and is running with a constant velocity of 2.6 km/h due east. Runner B is initially 5.4 km east of the flagpole and is running with a constant velocity of 8.6 km/h due west. What will be the distance of the two runners from the flagpole when their paths cross? ____km from the flagpole due from which of the following: west, east, north or south?

Answer 1

First, let's make a diagram to visualize the problem.

We know that, at the start, runners are 13.8 kilometers apart. So, the distance of runner A is going to be x, while the distance of runner B is going to be 13.8-x. Then, we use the equation of constant motion.

$t=\frac{d}{v}$

Let's express an equation for each runner using the given velocities and the expressions of the distances we defined before.

$\begin{gathered} A\colon t=\frac{x}{2.6} \\ B\colon t=\frac{13.8-x}{8.6} \end{gathered}$

Now we combine the equations to solve for x.

$\begin{gathered} \frac{x}{2.6}=\frac{13.8-x}{8.6} \\ 8.6x=2.6(13.8-x) \\ 8.6x=35.88-2.6x \\ 8.6x+2.6x=35.88 \\ 11.2x=35.88 \\ x=\frac{35.88}{11.2} \\ x\approx3.2\operatorname{km} \end{gathered}$

The distance of Runner A is 3.2 km.

Then, we subtract to find the position with respect to the flagpole.

$8.4km-3.2km=5.2\operatorname{km}$

Therefore, they will be 5.2 km west.