Question

Ali was driving to school, completes the average speed for his trip to be 20 km/h. On his return journey along the same route there is less traffic and average speed is 30 km/h. What is the average speed of Ali's trip ?

Answer 1

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Method I:  

Let the distance traveled by Abdul from home to school = s km
time taken to reach the school=t1 sec
For Return journey , Abdul cover distance =s km
time=t2 sec
∴ Average speed for forward journey[home - school ] = Total distance/ Total time.
20 km/h =s/t1
∴t1=s/20 h ------eq(1)
 Average speed for backward journey[school -home] = Total distance/ Total time.
30 km/h =s/t2
t2=s/30h -----eq(2)
Average distance for entire journey = Total distance/ Total time
                                                         =(s+s)/[s/20 +s/30]
                                                         =2s/s[1/20+1/30]
                                                          =2x20x30/50
                                                           =24 km/hr
Shortcut method : If equal distance are covered with speeds v1 and v2 then average distance=2v1v2/v1+v2
                           = 2x20x30/50
                            =24km/hr

∴ The average speed for Ali's trip is 24km/h

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