Question

A boy goes from his house to school by bus at a speed of $20km{h^{ - 1}}$ and returns back through the same route at a speed of $30km{h^{ - 1}}$. The average speed of his journey is:

Answer 1

Hint: In order to answer this question, first we will assume the distance between school and the house and then we will calculate the total time taken by the boy. And then we will also calculate the total distance covered by him according to the question. And finally we can find the average speed of his journey.

Complete step by step answer:
In the given question, first we will assume the distance between the school and the house is $x\,km$ .
Speed of the boy from house to school $ = 20km/hr$
Using the formula of time taken:
$ time = \dfrac{{distance}}{{time}}$
So, time taken $\dfrac{x}{{20}}hrs$ .
And, the speed of the boy from school to the house $ = 30km/hr$ .
So, time taken $ = \dfrac{x}{{30}}hrs$ .
Total time taken $ = \dfrac{x}{{20}} + \dfrac{x}{{30}} = \dfrac{x}{{12}}hrs$
And also, total distance covered by boy $ = x + x = 2xkm$
So, the average speed is:
$ = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{{2x}}{{\dfrac{x}{{12}}}} = 24km/hr$
Hence, the average speed of the boy’s journey is $24km/hr$.

Note: The cumulative distance travelled by the object in a given time period is the average speed. A scalar quantity is average speed. It has no direction and is expressed by the magnitude. Or in other words, the distance travelled in a given amount of time is measured by average speed, which is also known as the distance per time ratio. The average speed of an object indicates the (average) rate at which it travels a given distance, while its speed varies over time.