Multiple choice

An automobile went up a hill at a speed of $10\ km$ an hour and down the same distance at a speed of $20\ km$ an hour. The average speed for the round trip was

  1. $12\dfrac {1}{2} km/ hr$
  2. $13\dfrac {1}{3} km/ hr$
  3. $14\dfrac {1}{2} km/ hr$
  4. $15\ km/ hr$

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed for a round trip with equal distances is calculated using the harmonic mean formula: 2xy / (x + y). Plugging in 10 and 20 gives 2 * 10 * 20 / (10 + 20) = 400 / 30 = 13 1/3 km/hr.

AI explanation

Use the harmonic mean formula for average speed over equal distances: 2uv / (u + v). Plugging in the uphill and downhill speeds of 10 km/hr and 20 km/hr gives (2 * 10 * 20) / (10 + 20). This evaluates to 400 / 30, resulting in an average speed of 13 1/3 km/hr.

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