Multiple choice

A motor vehicle travelled the first third of a distance s at a speed of ${ v }{ 1 }=10$ kmph, the second third at a speed of ${ v }{ 2 }=20$ kmph and the last third at a speed of ${ v }_{ 3 }=60$ kmph. Determine the mean speed of the vehicle over the entire distance s.

  1. 15 kmph

  2. 12 kmph

  3. 10 kmph

  4. 18 kmph
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D Correct answer
Explanation

Mean speed = Total distance / Total time. Let total distance be 3d. Time = d/10 + d/20 + d/60 = (6d+3d+d)/60 = 10d/60 = d/6. Mean speed = 3d / (d/6) = 18 kmph.

AI explanation

Because the journey is divided into three equal parts, the mean speed is the total distance divided by the total time, calculated as 3s / (s/v1 + s/v2 + s/v3). Substituting the given values results in 3 / (1/10 + 1/20 + 1/60). Finding a common denominator of 60 gives 3 / (6/60 + 3/60 + 1/60) = 3 / (10/60), which equals 18 kmph.

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