📊 Average Speed

The only formula you always need: $\text{average speed}=\dfrac{\text{total distance}}{\text{total time}}$. Add up every kilometre, add up every hour (including any stop), then divide.

• Equal distances at two speeds $x$ and $y$ (a go-and-return trip, or first-half/second-half): use the harmonic mean $\dfrac{2xy}{x+y}$. It always sits a little BELOW the plain average $\dfrac{x+y}{2}$ — a handy way to strike off wrong options.

• A stop adds to time but not to distance, so the average always falls below the running speed.

• Unequal distances (e.g. 40% then 60%): the $\dfrac{2xy}{x+y}$ trick fails — go back to $\dfrac{\text{total distance}}{\text{total time}}$ with smart numbers.