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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 $40\, km \,h^{-1}$. What is the average speed(in $km\,h ^{-1}$) for Abdul's trip?
$20$
$44$
$24$
$34$
Solution
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 $v _{1 \,av }=20 \,km h ^{-1}$
Average speed from school to home $v _{2 \,av }=30 \,km\, h ^{-1}$
Also we know Time taken form Home to School $t _{1}= S / v_{1 \,av }$
Similarly Time taken form School to Home $t _{2}= S / v _{2 \,av }$
Total distance from home to school and backward = $2 \,S$
Total time taken from home to school and backward $(T)=S / 20+S / 30$
Therefore, Average speed $(v _{av})$ for covering total distance $(2\, S)=$ Total Dostance/Total Time
$=2\, S /(S / 20+S / 30)$
$=2 \,S /[(30\, S +20\, S ) / 600]$
$=1200\,S / 50 \,S$
$=24\, km\,h ^{-1}$
