Question

Jordan is very conscious about his health. He goes for a morning walk on a daily basis. He keeps a track of the time that he needs to cross different distances as tabulated below.
Miles Time (minutes)

$1.5$	$33$
$2$	$40$
$2.5$	$52$
$3$	$60$

On a Sunday, Jordan decides to cover $3.5$ miles. How much time in minutes Jordan needs to complete $3.5$ miles walk?

• A. $65$
• B. $70$
• C. $75$
• D. $80$

Answer 1

The correct option is B $70$

To predict the time required to complete $3.5$ miles, which is not included in the given data set, we first find out the trend line that best represents the data set.

Let's plot the given data set on a scatter plot diagram with miles covered (independent variable) on $x$-axis and time taken (dependent variable) on $y$-axis.

Logically, it is very clear that if Jordan wants to cover longer distance, the required time to cover will also be more.


In the above scatter plot, the cyan line represents the line of best fit, which passes though $(x_1,y_1)=(2,40)$ and $(x_2,y_2)=(3,60)$.

The slope of the line of best fit is
$m=\frac{y_2-y_1}{x_2-x_1}$
$\Rightarrow$ $m=\frac{60-40}{3-2}=\frac{20}{1}=20$

Hence, the equation of the line of best fit is

$y-y_1=m(x-x_1)$

$\Rightarrow y-40=20(x-2)$

$\Rightarrow y-40=20x-40$

$\Rightarrow y-40+40=20x-40+40$

$\Rightarrow y=20x$

By substituting the covering distance $x=3.5$ miles in the above equation of the line of best fit, we get the required time as

$y=20\times 3.5=70$ minutes

$\therefore$ Jordan needs $70$ minutes to complete $3.5$ miles walk, i.e., option (b.) is the correct one.