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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 30 km h^(-1). What is the average speed for Abdul's trip ?

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Answer Text

Answer :
average speed `=24 km h ^(-1)`
Solution :
The distance Abdul commutes while driving from Home to School = S <br> Let us assuem time taken by Abdul to commutes this distance = `t_(1)` <br> Distance Abdul commutes while driving from School to Home = S <br> Let us assume time taken by Abdul to commutes this distance = `t_(2)` <br> Average speed form home to school `v_(1av)` = 20 km `h_(-1)` <br> Average speed from school to home `v_(2av)` = 30 km `h^(-1)` <br> Also we know Time taken from Home to School `t_(1)=S//v_(1av)` <br> Similarly Time taken form School to Home `t_(2)=S//v_(2av)` <br> Total distance from home to school and backward = 2 S <br> Total time taken from home to school and backward (T) = S/20+S/30 <br> Therefore, Average speed (`V_(av)`) for covering total distance (2S) = Total Distance/Total Time <br> = 2S/(S/20+S/30) <br> = 2S/[(30S+20S)/600] <br> = 1200S /50S <br> = 24 km `h^(-1)`

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