Question

A car started at 9:00 a.m. from city A and stopped in city C at 10:00 a.m.. The diagram below shows the distance the car had traveled at different times.


Which of the following graph represents the proportional relationship between the distance the car has traveled and time taken by it? What will be the average speed of the car?
[Hint: Average speed of the car = Slope of the distance-time graph]

Answer 1

$\text{Detailed step-by-step solution:}$
Let $y$ represent the distance (in miles) traveled by the car,
and $x$ represent the time (in min) taken by it.
City A: $x=0$ min, $y=0$ miles
City B: $x=25$ minutes, $y=18.75$ miles
City C: $x=60$ minutes, $y=(18.75+26.25)$ miles $=45$ miles
The points on the graph which represents the cities will be:
City $\text{A(0, 0), City B(25, 18.75), City C(60, 45)}$
Plotting the graph using these points, we get:


The graph which is corresponding to the above graph is the graph given in option D.
$\text{Finding the slope of the graph:}$
Let’s consider two points $(60,45)$ and $(40,30)$ on the graph.
Slope of the graph $=\frac{Rise}{Run}$
$=\frac{45-30}{60-40}$
$=\frac{\text{15 miles}}{\text{20 minutes}}$
$=\frac{\text{15 miles}}{\frac{20}{60}hr}$ (since 1 hr = 60 minutes, 1 minute $=\frac{1}{60}$ hr)
$=\frac{\text{15 miles}}{\text{20 hr}}\times 60$
$=45miles/hr$
The average speed of the car = Slope of the graph
$\text{= 45 miles/hr}$
➡ Option D is correct.