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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?
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Solution
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).
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