Abdul, while driving to school, computes the average speed for his trip to be 20 km/h. On his return trip along the same route, there is less traffic and the average speed is 40 km/h. What is the average speed for Abdul’s trip?

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 }

\(\Rightarrow \) \( v_{av. trip} = \) = \( d+d \over ( \frac{d}{20} ) + ( \frac{d}{40} ) \) \( = 80 \over 3 \)