Question

Two cars started from the same position on a straight road. The first car covers 35 miles in every 40 minutes, while the distance traveled by the second car with time is shown by the graph below.


What will be the distance between the cars after 2 hours from the start of their journey?

• A. 90 miles
• B. 20 miles
• C. 105 miles
• D. 15 miles

Answer 1

The correct option is D 15 miles

$\text{Detailed step-by-step solution:}$
Let $Y$ represent the distance (in miles) traveled by the first car and y represent the distance (in miles) traveled by the second car,
and let $X$ represent the time (in min) taken by the first car and x represent the time (in min) taken by the second car.

$\text{Finding the equation for the first car:}$
As the first car travels 35 miles every 40 minutes; therefore, the distance and time are proportionally related.
And $Y=35$ miles at $X=40min.$
Constant of proportionality $=\frac{Y}{X}$
$=\frac{\text{35 miles}}{\text{40 minute}}$

$\frac{Y}{X}=\frac{35}{40}$

$\Rightarrow Y=\frac{35}{40}X$

$\text{Finding the distance covered by the first car after 2 hours:}$
$X=2hr=2\times 60min=120min$
$Y=\frac{35}{40}\times 120$
$\Rightarrow \text{Y = 105 miles}$

$\text{Finding the equation for the second car:}$
Since the graph is a straight line passing through the origin, the distance traveled by the second car and the time taken by it are proportionally related.
Let’s consider the point (80, 60) on the graph
I.e., at $x=80min,y=60miles.$
Constant of proportionality $=\frac{y}{x}$
$=\frac{\text{60 miles}}{\text{80 minute}}$
$\Rightarrow yx=\frac{60}{80}$
$\Rightarrow y=\frac{60}{80}x$

$\text{Finding the distance covered by the second car after 2 hours:}$
$x=2hr=2\times 60min=120min$
$y=\frac{60}{80}\times 120$
$\Rightarrow \text{y = 90 miles}$
Both the cars started from the same position, so the distance between them after two hours will be equal to the difference of the distance traveled by each car.
Distance between two cars = Distance traveled by the first car − Distance traveled by the second car
$=105$ miles $-90$ miles
$\text{= 15 miles}$

The distance between the cars after 2 hours from the start of their journeys will be 15 miles.
➡ Option B is correct.