Multiple choice

A person goes from point $P$ to point $Q$ covering $1/3$ of the distance with speed $10\ km/hr$, the next $1/3$ of the distance at $20\ km/hr$ and the last $1/3$ of the distance at $60\ km/hr$. The average speed of the person is

  1. $30\ km/hr$
  2. $24\ km/hr$
  3. $18\ km/hr$
  4. $12\ km/hr$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = Total distance / Total time. Let total distance = 3D. Time = D/10 + D/20 + D/60 = (6D + 3D + D) / 60 = 10D/60 = D/6. Average speed = 3D / (D/6) = 18 km/hr.

AI explanation

For a journey divided into equal parts traveled at different speeds, the average speed is the harmonic mean of the individual speeds: 3xyz / (xy + yz + zx). Substituting 10, 20, and 60 into the formula gives (3 * 10 * 20 * 60) / (10*20 + 20*60 + 60*10). The numerator becomes 36000 and the denominator becomes 2000, making the average speed 18 km/hr.

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