Multiple choice

A bus travels the first one third distance at a speed of $\displaystyle 10 km\ { h }^{ -1 }$, the next one third distance at a speed of $\displaystyle 20 km\ { h }^{ -1 }$ and the next one third distance at a speed of $\displaystyle 30 km\ { h }^{ -1 }$ .

  1. $\displaystyle 20 \quad { ms }^{ -1 }$
  2. $\displaystyle \frac { 50 }{ 11 } { ms }^{ -1 }$
  3. $\displaystyle \frac { 180 }{ 11 } { ms }^{ -1 }$
  4. $\displaystyle 30 \quad { ms }^{ -1 }$
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B Correct answer
Explanation

For equal distances, the average speed is the harmonic mean: 3 divided by (1/10 + 1/20 + 1/30), which equals 180/11 km/hr. Converting to m/s gives (180/11) × 5/18 = 50/11 m/s.

AI explanation

When equal distances are covered at different speeds, the average speed is calculated using the harmonic mean formula for three speeds. Let the total distance be 3d, so the total time taken is d/10 + d/20 + d/30 hours, which equals 11d/60 hours. The average speed is total distance divided by total time, giving 3d divided by 11d/60, which equals 180/11 km/hr. Converting this to meters per second by multiplying by 5/18 gives the final answer of 50/11 m/s.

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