The formula: count ÷ sum of reciprocals
For speeds of 60 and 40 (km/h) over equal distances: take the reciprocal of each (1/60 and 1/40), add them together (1/60 + 1/40 ≈ 0.041667), then divide the count (2) by that sum: 2 ÷ 0.041667 = 48.
Why it's not simply the average of 60 and 40
The simple average of 60 and 40 is 50 — but that overstates the true average speed. More time is actually spent traveling at the slower 40 speed (since covering the same distance takes longer at a lower speed), so the true average weights toward the slower value, which is exactly what the harmonic mean's 48 correctly reflects.
A second example, with the numbers 4 and 9
For 4 and 9: 1/4 + 1/9 ≈ 0.361111, and 2 ÷ 0.361111 ≈ 5.538462 — noticeably lower than either the arithmetic mean (6.5) or the geometric mean (6) of the same two numbers.
When to reach for harmonic mean specifically
Harmonic mean is the right tool specifically when averaging rates defined over a fixed, equal quantity — equal distances for speed, equal work for rates of work, and similar cases. For most other kinds of averaging, arithmetic or geometric mean is more appropriate, as the companion article comparing all three means explores.