Question

A car travels a distance d on a straight road in two hours and then returns to the starting point in the next three hours. Its average speed is:
A. $\dfrac{d}{5}$
B. $\dfrac{2d}{5}$
C. $\dfrac{d}{2}+\dfrac{d}{3}$
D. None of these

Answer 1

We need to find the average distance of a car when it travels a distance d and returns to its starting point. Time taken by the car for covering a distance d and return to its starting point is given. We know that average speed is the ratio of total distance to total time taken. By calculating total distance and total speed we get the average speed of the car.

Formula Used:
$\text{average speed=}\dfrac{\text{total distance}}{\text{total time}}$

Complete step-by-step answer :
We have a car that travels a distance d on a straight road.
The time taken to travel d distance is given to be 2 hours.
After travelling d distance the car returns back to the starting point.
Therefore the total distance traveled by the car will become, d + d = 2d
The time taken by the car to return to the initial point is given as 3 hours.
We are asked to calculate the average speed of the car.
We know that average speed is can be calculated by the equation,
$\text{average speed=}\dfrac{\text{total distance}}{\text{total time}}$
Here the total distance traveled by the car = 2d
Total time taken by the car = 2 + 3 = 5 hours
Therefore we get the average speed of the car as,
$\text{avg}\text{.speed=}\dfrac{2d}{5}$
Hence the correct answer is option B.

Note : Here we are calculating the average velocity of the car. Therefore we are considering the total distance traveled by the car, not the total displacement of the car.
We know that the total displacement of the car is zero, because the car returns to its starting. But the total distance traveled by the car is not zero.