Question

A boy covers half of his journey with a uniform speed of u and the other half with a uniform speed of v. What is the average speed for the whole journey?

Answer 1

Let total distance be S.
Boy covers distance S/2 with speed u then time taken by him to cover this distance would be T₁ =S/2u.
Again boy covers rest of the distance S/2 with speed v then time taken by him to cover this distance would be T₂ =S/2v.
So total time taken by boy to cover the distance S is T = T₁ + T₂.
Total time T= S/2 (1/u +1/v) = s(u+v)/2uv.
And average speed = S/T = 2uv/(u+v).