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Question
A body covers half the distance with the speed A and the other half with speed B. What will be the average speed for the whole journey?
Solution
Let total distance be S.
Boy covers distance S/2 with speed A then time taken by him to cover this distance would be T1 =S/2A.
Again boy covers rest of the distance S/2 with speed B then time taken by him to cover this distance would be T2 =S/2B.
So total time taken by boy to cover the distance S is T = T1 + T2.
Total time T= S/2 (1/A +1/B) = s(A+B)/2AB.
And average speed = S/T = 2AB/(A+B).
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