An aeroplane flies around a square,the sides | vedclass

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Question

(C) The average speed for equal distances covered at different speeds is given by the harmonic mean of the speeds.Let the side length be $d = 100 	ex

Vedclass · Accepted Answer

$192$

Vedclass · Answer

(C) The average speed for equal distances covered at different speeds is given by the harmonic mean of the speeds.Let the side length be $d = 100 	ext{ miles}$.The time taken for each side is $t_i = \frac{d}{v_i}$.Total distance $D = 4d$.Total time $T = \frac{d}{100} + \frac{d}{200} + \frac{d}{300} + \frac{d}{400} = d \left( \frac{1}{100} + \frac{1}{200} + \frac{1}{300} + \frac{1}{400} ight)$.Average speed $V_{avg} = \frac{D}{T} = \frac{4d}{d \left( \frac{1}{100} + \frac{1}{200} + \frac{1}{300} + \frac{1}{400} ight)}$.$V_{avg} = \frac{4}{\frac{12+6+4+3}{1200}} = \frac{4 	imes 1200}{25} = \frac{4800}{25} = 192 	ext{ mph}$.Hence,$(c)$ is the correct answer.

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