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

Let total distance = x            
  $$\begin{gathered} speed=\frac{dis\tan ce}{time} \\ time=\frac{dis\tan ce}{speed} \\ Total time taken=\frac{x}{3u}+\frac{x}{3v}+\frac{x}{3w} \\ total time taken=x\left(\frac{vw+uw+uv}{3uvw}\right)---\left(1\right) \end{gathered}$$
 $$\begin{gathered} Average speed =V_{av}=\frac{totaldisatncetravelled}{totaltimetaken}---\left(2\right) \\ substitute equation \left(1\right) in \left(2\right) \end{gathered}$$
$V_{av}=\frac{x}{x\left(\frac{vw+uw+uv}{3uvw}\right)}$  
   $Average speed=\frac{3uvw}{vw+uw+uv}$