Question

A body goes from P to Q with a uniform speed of u and immediately returns back to P at a uniform speed of v. What is the average speed for the whole journey?

Answer 1

Let S be the distance between P and Q.
Body covers forward journey distance S (P to Q) with speed u then time taken by him to cover this distance would be T₁ =S/u.
Again body covers backward journey distance S (Q to P) with speed v then time taken by him to cover this distance would be T₂ =S/v.
So total time taken by body to cover the distance S is T = T₁ + T₂.
Total time T= S (1/u +1/v) = s(u+v)/uv.
And average speed = 2S/T = 2uv/(u+v).