A boy goes to a school from his home at a speed of  x  km/hr and comes back at a speed of y km/hr, then the average speed is given by

Let the distance between the school and the home be s km. Then, total time taken in going to and coming from the school is given by    t=sx+sy⇒t=x+yxy s⇒st=xyx+y   Average speed =2st=2xyx+y= H. M. of x and y