Answer:
Lauren will finish the race faster 7 seconds faster, and 14 meters ahead.
Explanation:
To answer this question, I will use the strategy of finding the slope of each of the proportional relationships (y = 8x for Lauren's run and y = ?x for Amani's run). The slope represents the rate at which the distance changes for each unit of time, so the person with the greater slope will finish the race faster.
To find the slope of Amani's run, I will use the tool of point-slope form, which is y - y1 = m(x - x1). I will plug in the coordinates for the second point listed in the table for Amani's run (5 seconds and 30 meters) to get y - 30 = m(5 - x1). Since I don't know the value of x1, I will solve for it in terms of m. I get x1 = 5 - (30/m).
Next, I will plug in the coordinates for the first point listed in the table for Amani's run (3 seconds and 18 meters) into the equation y - 30 = m(5 - (30/m)). I get 18 - 30 = m(5 - (30/m)). Solving for m, I find that Amani's run has a slope of m = -6.
Since Lauren's run has a slope of 8 and Amani's run has a slope of -6, Lauren will finish the race faster. To find out by how much, I will use the tool of proportional reasoning. Since the slope represents the rate at which the distance changes for each unit of time, the difference in the slopes (8 - (-6)) represents the difference in the rate at which the distance changes for each unit of time between the two runs. The difference is 14, so Lauren will finish the race 14 meters ahead of Amani for each second that they run. Since the race is 100 meters long, Lauren will finish the race approximately 7 seconds faster than Amani.