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

average speed `=24 km h ^(-1)`

Explanation

The distance Abdul commutes while driving from Home to School = S
Let us assuem 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 form 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 from Home to School `t_(1)=S//v_(1av)`
Similarly Time taken form School to Home `t_(2)=S//v_(2av)`
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 (2S) = Total Distance/Total Time
= 2S/(S/20+S/30)
= 2S/[(30S+20S)/600]
= 1200S /50S
= 24 km `h^(-1)`