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Question

 Abdul while driving to school computes the average speed for his trip to be 20 km per hour  on his return trip along the same route there is less traffic and the average speed is 30 km per hour what is the average speed for Abdul trip


Solution

Given :

 

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 Abdul's trip is 24km/h



 

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