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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?
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Solution
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).
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