Question

Abdul, while driving to school, computes the average speed for his trip to be $20$ $km\, h^{–1}$. On his return trip along the same route, there is less traffic and the average speed is $30$ $km \,h^{–1}$. What is the average speed for Abdul’s trip?

Answer 1

The distance Abdul commutes while driving from Home to School = $S$
Let us assume time taken by Abdul to commutes this distance = $t_1$
Distance Abdul commutes while driving from School to Home = $S$
Let us assume time taken by Abdul to commutes this distance = $t_2$
Average speed from home to school $v_{1av}$ = $20$ $km\, h^{-1}$
Average speed from school to home $v_{2av}$ = $30$ $km\, h^{-1}$
Also we know Time taken form Home to School $t_1$ = $\frac{S}{ v_{1av}}$
Similarly Time taken form School to Home $t_2$ = $\frac{S}{v_{2av}}$
Total distance from home to school and backward = $2$ $S$
Total time taken from home to school and backward $(T)$ = $\frac{S}{20}+ \frac{S}{30}$
Therefore, Average speed $(V_{av})$ for covering total distance $(2S)$
= $\frac{Total \,Dostance}{Total \,Time}$

= $\frac{2S }{ \bigg(\frac{S}{20} +\frac{S}{30}\bigg)}$

= $\frac{2S }{ \bigg[\frac{(30S+20S)}{600}\bigg]}$

= $\frac{1200\,S }{ 50\,S}$

= $24\; km\,h^{-1}$