Question

Abdul, while driving to school, computes the average speed for his trip to be $20km{h}^{-1}$. On his return trip along the same route, there is less traffic and the average speed is $40km{h}^{-1}$. What is the average speed for Abdul’s trip?

Answer 1

Let the distance Abdul commutes while driving from home to school $=s$
Let us assume time taken by Abdul to commute this distance $=t_1$
Distance Abdul commutes while driving from school to home $=s$
Let us assume time taken by Abdul to commute this distance $=t_2$
Average speed from home to school $v_{1avg}=20km{h}^{-1}$
Average speed from school to home $v_{2avg}=40km{h}^{-1}$
Also we know time taken from home to school $t_1=\frac{s}{v_{1avg}}$
Similarly, time taken from school to home $t_2=\frac{s}{v_{2avg}}$
Total distance from home to school and backward $=2s$
Total time taken from home to school and backward $\left(T\right)=\frac{S}{20}+\frac{S}{40}$
Therefore, average speed$\left(v_{avg}\right)$ for covering total distance $\left(2s\right)=\frac{TotalDistance}{TotalTime}$
$=\frac{2s}{\frac{s}{20}+\frac{s}{40}}$
$=26.67km{h}^{-1}$