Multiple choice

A boy walks to his school at a distance of $6\;km$ with a speed of $2.5\;km/h$ and walks back with a constant speed by $4 \;km/h$. His average speed for trip expressed in $km/h$ is

  1. $\displaystyle \frac{24}{13}$
  2. $\displaystyle \frac{40}{13}$
  3. $3$
  4. $4.8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed = Total distance / Total time. Total distance = 6 + 6 = 12 km. Time 1 = 6 / 2.5 = 2.4 hours. Time 2 = 6 / 4 = 1.5 hours. Total time = 3.9 hours. Average speed = 12 / 3.9 = 120 / 39 = 40 / 13 km/h.

AI explanation

When equal distances are travelled at two different speeds, apply the harmonic mean formula for average speed: 2xy divided by (x + y). Substituting the given values gives (2 * 2.5 * 4) divided by (2.5 + 4). This simplifies to 20 divided by 13, resulting in an average speed of 40/13 km/h.

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