Running Rates and Linear Relationships Math 8 Unit 4 Think about the affect a running rate has on the relationship between the time run and the distance run. We will use this data to investigate linear relationships using tables, graphs, and equations.
Problem: Below are Alberto, Tracy, and Tiana’s running rates. Name Alberto Tracy Tiana
Running Rate 2 meters per second 3 meters per second 3.5 meters per second
A. 1. Make a table showing the distance run by each student for the first ten seconds. How does the running rate affect the data?
2. Graph the time and distance of each student on the same coordinate axis. Use a different color for each student’s data. How does the running rate affect the line?
3. Write an equation that shows the relationship between the time “t” and the distance “d” run for each student. How is the running rate represented in the equation?
B. For each student: 1. If “t” increases by 2 seconds, how much does the distance change? How is this change represented in a table? In a graph? 2. If “t” increases by 10 seconds, how much does the distance change? How is this change represented in a table? A graph? 3. What is the running rate per minute? The running rate per hour?
C. Four other friends who are part of the Run-a-Thon made the following representations of their data. Are any of these relationships linear relationships? Are any of them functions? Explain.
Joe’s Running Rate Time (seconds) 0 1 2 3 4 5
Distance (meters) 0 2 9 11 20 25
Beth’s Running Rate Time (seconds) 0 2 4 6 8 10
Distance (meters) 0 3 6 9 12 15
Billie’s Running Rate D= 2.25 t D represents distance t represents time
Bob’s Walking Rate t= 100/r t represents time r represents rate