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Aptitude Topics

Average Speed

Average speed is not a simple average of your different speeds. It measures the total distance covered across an entire multi-leg journey divided by the total time spent traveling.

Fundamental Principles

Average Speed

The unified rate of progress across a compound trip, defined by the formula: $S_{\text{avg}} = \frac{\text{Total Distance Covered}}{\text{Total Time Taken}}$.

Essential Formulation Tips

  • Never simply add your speeds together and divide by two; this approach ignores how long you traveled at each specific speed.
  • If a journey is divided into equal distance legs, you can bypass the actual distance values entirely and use harmonic mean shortcuts instead.

Shortcut Execution Techniques

  • The Equal-Distance Harmonic Shortcut: If an object covers a distance at speed $x$ and then travels an equal distance at speed $y$, the unified average speed for the entire trip is: $S_{\text{avg}} = \frac{2xy}{x+y}$.

Contextual Inquiries (FAQs)

Q: Can I use the harmonic mean shortcut formula if the travel distances for each leg are different?

A: No. The $\frac{2xy}{x+y}$ shortcut only works when the distances for each leg are identical. If the distances differ, you must calculate total distance and total time manually.