For two positive unequal speeds v₁ and v₂, the average speed for equal distances and the average speed for equal times become equal only when:
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Question

For two positive unequal speeds v₁ and v₂, the average speed for equal distances and the average speed for equal times become equal only when:

G1 Physics · Accepted Answer

Equal-distance average speed: 2v₁v₂/(v₁+v₂). Equal-time average speed: (v₁+v₂)/2. Equating them: 4v₁v₂ = (v₁+v₂)² ⇒ (v₁−v₂)² = 0 ⇒ v₁=v₂.