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Answer :
Let distance travelled to reach the school = d km = distance traveled to reach home
and time taken to reach school = \( t_1 \) and time taken to reach home =\( t _2 \)
Average speed while going to school = 20 kmph
\(\therefore \) \( 20 = \) \( d \over t_1 \) \(\Rightarrow \) \( t_1 = \) \( d \over 20 \) ..... -(i)
Average speed while going home = 30 kmph
\(\therefore \) \( 40 = \) \( d \over t_1 \) \(\Rightarrow \) \( t_1 = \) \( d \over 40 \) ...... -(ii)
Now, the average speed for the entire trip = \( Total \ distance \ covered \ in \ the \ trip \ \over Total \ time \ taken \)
\(\therefore \) \( v_{av. trip} = \) \( d+d \over t_1 + t_2 \) {\(\because \) total distance = distance travelled to reach the school + distance traveled to reach home }
\(\Rightarrow \) \( v_{av. trip} = \) = \( d+d \over ( \frac{d}{20} ) + ( \frac{d}{40} ) \) \( = 80 \over 3 \)