Um, it is true, because it matters critically what the units are. In particular, it matters whether the distance term is in the numerator or the denominator: as Tanstaafl said, it's about commutativity -- or, put differently, it's because the reciprocal of the sum is not the same as the sum of the reciprocals, but a sum of sums works both ways round.

Try it: I go somewhere 100km away and come back, my fuel consumption on the way there is 2 litres/100km, for the whole 200km trip it's 10 litres/100km. That means I use 20 litres for the whole trip, 2 litres on the way there, must have been 18 on the way back -- for a consumption of 18 litres/100km. And 18 is exactly what simple linear averaging would also have come out with.

Peter