Write two equations describing Bernie and Wendel's runs.
No, see solution.
Practice makes perfect
The distance each person runs depends on how many seconds they run. Therefore, time in seconds is the independent variable, and meters is the dependent variable.
Since Bernie and Wendel run at a constant rate, their races can be represented by linear equations in slope-intercept form.
y=mx+bIn this equation, m is the line's slope and b is the y-intercept. To draw the graphs, we need at least two points. From the exercise, we know that Bernie starts from the starting line while Wendel has a 9 meters head start. This means the y-intercept of Bernie and Wendel is at (0,0) and (0,9), respectively.
From the exercise, we also know that Bernie runs 9 meters in 4 seconds and Wendel runs 2 meters every second. With this information, we can find a second point through which each graph passes, and thereby draw each function.
Since Bernie runs at a faster rate then Wendel, 94>2, he will sooner or later catch up with Wendel. By equating Wendel's and Bernie's equations, we can determine when Bernie catches Wendel.
After 36 seconds, Bernie will have caught up with Wendel. By substituting this number in either equation, we can find how far they have run at that time.
