Linear Functions

Question

Cameron and David are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Cameron is 700 miles away from the stadium and David is 850 miles away from the stadium. Cameron is driving along the highway at a speed of 25 miles per hour and David is driving at speed of 50 miles per hour. Let C represent Cameron's distance, in miles, away from the stadium t hours after noon. Let D represent David's distance, in miles, away from the stadium t hours after noon. Graph each function and determine the number hours after noon, t, when Cameron and David are the same distance from the stadium

Answer 1

Graph distance on the y axis, hours after noon on the x axis

C=700-25t

D=850-50t

t=6 is when both are the same distance away, 550 miles.

C has y intercept of 700 and x intercept of 28

D has y intercept of 850 and x intercept of 17

both are downward sloping lines. They intersect at (6,550)

700-25t = 850-50t

50t-25t = 850-700

25t = 150

t =150/25 = 6 hours after noon: 6:00 PM

they have a long drive to go

Answer 2

This problem is pretty straight forward.

You will first create two functions, one for Cameron and one for David, both with the variable of time (t) as their input. Since Cameron is moving at 25 mph and starts 700 miles away from the stadium, and because he is heading towards the stadium, his function would look like this:

1. C(t) = 700 - 25t

Since David is moving at 50 mph and starts 850 miles away from the stadium, and because he is also heading towards the stadium, his function would look like this:

1. D(t) = 850 - 50t

Once you have these functions, inputting hours to determine distance away from the stadium and graphing becomes pretty simple. The answer to the problem is when (t on the x-axis) the two lines intersect.