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# 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 }

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