Question

The graph shows the distance run and the time taken by the two athletes in a marathon. Which athlete runs faster?

• A. Both run at the same speed
• B. Athlete $Z$
• C. Cannot be determined from the given data
• D. Athlete $Y$

Answer 1

The correct option is D Athlete $Y$

We know that the slope of each line represents its unit rate which is the speed of runners in the given case.
From the graph,
The speed of athlete $Y=\frac{5.25-3.5}{45-30}=\frac{1.75}{15}\simeq 0.116$
The speed of athlete $Z=\frac{5-3}{60-36}=\frac{2}{24}\simeq 0.0833$
Since the speed of athlete $Y>$ speed of athlete $Z$,
$\therefore$ Distance per unit time of athlete $Y$ is greater.
Thus, athlete $Y$ runs faster.
Note: We can also find the faster runner by just looking at the steepness of both lines. Both the lines are straight and going through the origin, therefore the slope represents the unit rate ($y$ per unit of $x)$. Since the line representing athlete $Y$ is steeper, hence he is faster than $Z$.