Question

A body covers one third of its journey with speed u, next one third with speed v and last one third with speed w. calculate the average speed of the body during the entire journey.

Answer 1

let the total distance be x
case1 
d=1/3x
s=u
t=d/t=1x/3u

case 2
d=1/3 x
s=v
t=1x/3 v

case3
d=`1/3 x
s=w
t=1 x/3w
  total d=x
  total time=1/3u+1/3v+1/3w=ux+vx+wx/3
avg speed= total distance/total time taken
                =x/ux+vx+wx/3
                =x/x(u+v+w)/3
   solving it....... 
 avg speed=3/u+v+w