Why Is a Round Trip’s Average Speed Not the Simple Average?

Suppose a 60-kilometre trip is travelled at 60 km/h on the way out and 40 km/h on the way back. Simply averaging the two speeds gives 50 km/h, but the average speed for the whole journey is actually 48 km/h.

Average speed is always total distance divided by total elapsed time. The outward leg takes one hour and the return leg takes 1.5 hours. The car therefore covers 120 kilometres in 2.5 hours: 120 ÷ 2.5 = 48. Although the distances are equal, the slower leg occupies more time, so it has more influence on the overall average.

The simple arithmetic mean works when each speed is maintained for the same amount of time. If a car travels at 60 km/h for one hour and 40 km/h for one hour, it covers 100 kilometres in two hours, averaging 50 km/h. Equal-distance legs instead produce a harmonic mean, but remembering the label is less useful than reliably adding distance and time separately.

Average speed should also be distinguished from average velocity. On a round trip back to the starting point, displacement is zero, so average velocity is zero. The car has nevertheless travelled 120 kilometres, and its average speed remains 48 km/h.

https://openstax.org/books/college-physics-2e/pages/2-3-time-velocity-and-speed