Question

camden and alexander are both driving along the same highway in two different cars to a stadium in a distant city. at noon, camden is 600 miles away from the stadium and alexander is 1000 miles away from the stadium. camden is driving along the highway at a speed of 25 miles per hour and alexander is driving at speed of 50 miles per hour. let c represent camden’s distance, in miles, away from the stadium t hours after noon. let a represent alexander’s distance, in miles, away from the stadium t hours after noon. graph each function and determine how far both camden and alexander are from the stadium at the moment they are an equal distance from the stadium.
click twice to plot each line. click a line to delete it.

Explanation:

Step1: Define Camden's distance function

Camden starts 600 miles away, moving closer at 25 mph.
$C(t) = 600 - 25t$

Step2: Define Alexander's distance function

Alexander starts 1000 miles away, moving closer at 50 mph.
$A(t) = 1000 - 50t$

Step3: Set distances equal, solve for $t$

Set $C(t)=A(t)$ to find when distances match.
$$600 - 25t = 1000 - 50t$$
$$-25t + 50t = 1000 - 600$$
$$25t = 400$$
$$t = \frac{400}{25} = 16$$

Step4: Calculate distance at $t=16$

Substitute $t=16$ into $C(t)$ (or $A(t)$).
$C(16) = 600 - 25(16) = 600 - 400 = 200$

Answer:

200 miles