Multiple choice

A car travels the first half of the distance between two places with a speed of $60kmp$. The speed of the car for the rest of the distance so that its average speed becomes $90kmph$.

  1. $60\ kmph$
  2. $90\ kmph$
  3. $120\ kmph$
  4. $180\ kmph$
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D Correct answer
Explanation

Let the total distance be 2d. The total time is d/60 + d/v, while the average speed is 90 kmph. Thus 2d/(d/60 + d/v) = 90, which gives v = 180 kmph. Equal distances require using the harmonic mean, not the ordinary arithmetic mean.

AI explanation

Assume the total distance is 2x, so each half is x, and let the unknown return speed be v. The average speed formula gives 90 = 2x / (x/60 + x/v). Solving the equation 1/90 = 1/120 + 1/v for v reveals the required speed. The required speed for the rest of the distance is 180 kmph.

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