Question

A body covers 0ne third of its journey with speed "u" , next one third with speed "v" and the last onethird with speed "w" . Calculate the average speed of the body during the entire journey.​

Answer 1

$let \: total \: distance \: = 3x. \: then \\ total \: time \: taken = \frac{x}{u} + \frac{x}{v} + \frac{x}{w} = x( \frac{vw + uw + uv}{uvw}) \\ average \: speed = \frac{total \: distance \: travelle}{total \: time \: taken} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3x}{ \frac{vw + uw + uv}{uvw}x } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3uvw}{uv + vw + uw}$

Answer 2

Answer:

a body covers one third of its journey with speed u and next third with speed v and last third with speed w the time is equal to distance upon speed when a body covers one third of its journey with speed time U.