Question

Abdul while driving to school computes the average speed for his trip to be 20 km h-1 on his return trip along the same route there is less traffic and the average speed is 30 km h-1 what is the average speed for abdul's trip

Answer 1

Method is this:
Let the distance traveled by Abdul from home to school = s kmtime taken to reach the school=t1 secFor Return journey , Abdul cover distance =s kmtime=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/t2t2=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/hrShortcut 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