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

• A. $24km{h}^{-1}$
• B. $25km{h}^{-1}$
• C. $20km{h}^{-1}$
• D. $30km{h}^{-1}$

Answer 1

The correct option is A $24km{h}^{-1}$

Let ‘$s$’ be the distance between house and the school.
Here, total distance covered by bus is $=2s$
Time incurred while travelling from house to school,
Time $\left(t_1\right)=\frac{\text{Distance}\left(s\right)}{\text{speed}\left(v_1\right)}$

$t_1=\frac{s}{20km{h}^{-1}}$

Time incurred while travelling from school to house,
Time $\left(t_2\right)=\frac{\text{Distance}\left(s\right)}{\text{Speed}\left(v_2\right)}$

$t_2=\frac{s}{30km{h}^{-1}}$

Total time taken $=t_1+t_2=\frac{s}{20}+\frac{s}{30}=\frac{5s}{60}$

We know,

$\text{Average speed}=\frac{\text{Total distance covered}}{\text{Total time taken}}$

$\text{Average speed}=\frac{2s}{\frac{5s}{60}}=24km{h}^{-1}$

Therefore, the average speed is $24km{h}^{-1}$.

So, option (a) '$24km{h}^{-1}$' is correct.