Question

comparing two linear functions (context - graphically)
score 4/5 penalty: none
question
anthony and riley are both driving along the same highway in two different cars to a stadium in a distant city. at noon, anthony is 800 miles away from the stadium and riley is 500 miles away from the stadium. anthony is driving along the highway at a speed of 50 miles per hour and riley is driving at speed of 25 miles per hour. let a represent anthony’s distance, in miles, away from the stadium t hours after noon. let r represent riley’s distance, in miles, away from the stadium t hours after noon. graph each function and determine the number hours after noon, t, when anthony and riley are the same distance from the stadium.
click twice to plot each line. click a line to delete it.
answer attempt 1 out of 2
answer:
hours per mile
hours
miles per hour
miles

Explanation:

Step1: Define the distance functions

Anthony's distance from the stadium: At noon (\(t = 0\)), he is 800 miles away, and he drives at 50 miles per hour towards the stadium. So his distance function is \(A(t)=800 - 50t\) (since distance decreases as he drives towards the stadium).

Riley's distance from the stadium: At noon (\(t = 0\)), she is 500 miles away, and she drives at 25 miles per hour towards the stadium. So her distance function is \(R(t)=500 - 25t\).

Step2: Set the functions equal to find \(t\)

We want to find when \(A(t)=R(t)\), so:

\(800 - 50t=500 - 25t\)

Subtract \(500\) from both sides:

\(800 - 500- 50t=500 - 500- 25t\)

\(300 - 50t=- 25t\)

Add \(50t\) to both sides:

\(300 - 50t + 50t=- 25t + 50t\)

\(300 = 25t\)

Divide both sides by 25:

\(t=\frac{300}{25}=12\)

Answer:

12 hours