A bus covers the first half of a certain distance with speed v₁ and the second half with a speed v₂. The average speed during the whole journey is:
- A(2 v₁ v₂)/(v₁+v₂)
- B(v₁+v₂)/2
- C(v₁ v₂)/(v₁+v₂)
- D√(v₁ v₂)
Show answer and explanation
Correct answer: (a) (2 v₁ v₂)/(v₁+v₂)
Explanation
For equal half-distances, average speed = total distance ÷ total time, not the simple mean of the two speeds.
With each half = d: time = d/v₁ + d/v₂, so average speed = 2d ÷ (d/v₁ + d/v₂).
Simplifying gives the harmonic mean 2v₁v₂/(v₁+v₂).