Finding Distance of Two Runners with Velocity and Acceleration | Help Needed

[MeganH]

Runner A is initially 6.0 km west of a flagpole and is running with a constant velocity of 9.0 km/h due east. Runner B is initially 5.0 km east of the flagpole and is running with a constant velocity of 8.0 km/h due west. What will be the distance of the two runners from the flagpole when their paths cross?

 

[johnsonandrew]

Write an equation for each runner, solve for time, then plug time into one of the equations to get distance. Use the same method for the other problem you posted.

 

[m2003]

To find the distance of the two runners from the flagpole when their paths cross, we can use the formula d = vt, where d is the distance, v is the velocity, and t is the time. In this case, we have two runners with different velocities and starting positions, so we will need to use a system of equations to solve for the time when their paths cross.

First, let's define some variables:
t = time when the paths cross
dA = distance of Runner A from the flagpole
dB = distance of Runner B from the flagpole

Using the formula d = vt, we can write the following equations:
dA = 9.0t + 6.0
dB = -8.0t + 5.0

Since we want to find the time when their paths cross, we can set these two equations equal to each other and solve for t:
9.0t + 6.0 = -8.0t + 5.0
17.0t = -1.0
t = -1.0/17.0 ≈ -0.06 hours

We can see that the time when their paths cross is negative, which means it has already happened. To find the distance, we can plug this value of t into either of the original equations:
dA = 9.0(-0.06) + 6.0 ≈ 5.4 km
dB = -8.0(-0.06) + 5.0 ≈ 5.48 km

Therefore, when their paths cross, Runner A will be approximately 5.4 km east of the flagpole and Runner B will be approximately 5.48 km west of the flagpole. The total distance between them will be the sum of these two distances, which is approximately 10.88 km.