Question

explain how you know which one is the slowest three runners are training for a marathon. One day, they all ran about 10 miles, each of their own constant speed. Which graph shows how long in minutes it takes Runner 1 to run X miles. the equation that relates to runner 2's distance in miles with time in minutes is T equals 8.5 d. runner 3's information is in the table: distance (miles) time(minutes)2 184 366 548 7210 90

Answer 1

Looking at the graph of runner 1, the y axis contains the time in minutes while the x axis contains the number of miles. To determine the number of minutes it took runner 1 to run 1 mile, we would determine the slope of the graph.

Slope = (y2 - y1)/(x2 - x1)

From the graph,

if x1 = 2, then y1 = 20

if x2 = 4, y2 = 40

Slope = (40 - 20)/(4 - 2) = 20/2 = 10

Runner 1 ran 1 mile in 10 minutes

For runner 2, the equation is

t = 8.5d where d is distance

If d = 1, then

t = 8.5 * 1 = 8.5

Runner 2 ran 1 mile in 8.5 minutes

For runner 3,

If x1 = 2, y1 = 18

if x2 = 4, y2 = 36

Slope = (36 - 18)/(4 - 2) = 18/2 = 9

Runner 3 ran 1 mile in 9 minutes

Thus, the slowest runner is runner 1