What is Average speed?

Example 52.9 (The trap, sprung)

A cyclist rides $60\,\mathrm{km}$ out at $30\,\mathrm{km}/\mathrm{h}$, and the same $60\,\mathrm{km}$ home at $20\,\mathrm{km}/\mathrm{h}$. “Average: $25\,\mathrm{km}/\mathrm{h}$”? Check honestly. Out: $t = 60 \div 30 = 2$ hours. Home: $t = 60 \div 20 = 3$ hours. Whole journey: $120\,\mathrm{km}$ in $5$ hours — $v_{\text{average}} = 24\,\mathrm{km}/\mathrm{h}$. The slow half claimed three hours of the five, and dragged the average below the midpoint. The faster you go on one half, the less time that half even exists.

Example 5.8 (Some speeds worth knowing)

A brisk walk: $1.5\,\mathrm{m}/\mathrm{s} \times 3.6 = 5.4\,\mathrm{km}/\mathrm{h}$. A city car at $54\,\mathrm{km}/\mathrm{h}$: $54 / 3.6 = 15\,\mathrm{m}/\mathrm{s}$ — about $15\,\mathrm{m}$ covered every second, worth remembering before stepping off a kerb. Sound in air: $340\,\mathrm{m}/\mathrm{s} \times 3.6 = 1224\,\mathrm{km}/\mathrm{h}$.

Example 5.9 (A hike with a break)

A hiker covers $12\,\mathrm{km}$ in $2\,\mathrm{h}$ of walking, then rests for $1\,\mathrm{h}$, then covers $6\,\mathrm{km}$ in the final $1.5\,\mathrm{h}$. Average speed over the whole outing:

The average counts all the elapsed time, breaks included — it is generally not the average of the speeds of the separate legs.