Question

Question 3
Abdul, while driving to school, computes the average speed for his trip to be $20kmph$. On his return trip along the same route, there is less traffic and the average speed is $40kmph$. 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 back from school to home $=s$
Let us assume time taken by Abdul to commute this distance $=t_2$
Average speed from home to school $v_{1avg}=20kmph$
Average speed from school to home $v_{2avg}=40kmph$
We know, $time=\frac{distance}{speed}$
Therefore, time taken from home to school $t_1=\frac{s}{v_{1avg}}=\frac{s}{20}$
Similarly, time taken from school to home $t_2=\frac{s}{v_{2avg}}=\frac{s}{40}$
Total distance from home to school and backward $=2s$
Total time taken from home to school and backward $T=t_1+t_2=\frac{s}{20}+\frac{s}{40}$
Therefore, average speed$\left(v_{avg}\right)$ for covering total distance $2s,v_{avg}=\frac{TotalDistance}{TotalTime}$
$=\frac{2s}{\frac{s}{20}+\frac{s}{40}}$
$=26.67kmph$