William Naismith was a Scottish mountaineer, and in 1892 he wrote down the sentence that still plans hill days: allow an hour for every three miles on the map, plus an hour for every 2,000 feet of ascent. The metric habit rounds it to $t = \dfrac{d}{5} + \dfrac{h}{600}$ — t equals d over five, plus h over six hundred.

The letters: $t$ is the walking time in hours; $d$ is the route distance in kilometres, measured on the map; $h$ is the total ascent in metres. The 5 and the 600 are not adjustable parameters — they ARE the rule. Change them and it is somebody else's rule with Naismith's name on it. Note also that $h$ is ascent only: descent is not credited, and the basic rule has no negative climb.

Carry it in a form you can use while walking: 12 minutes per kilometre, plus 6 minutes per 60 m of climb. The classic sanity check is 10 km on the flat coming out at almost exactly 2 hours — if your own answer surprises you, the units on $d$ and $h$ are the first place to look.

The other half of this lesson is the version with no assumptions in it: $t = \dfrac{d}{V_g}$, time equals distance over the speed made good. $V_g$ is what the party actually achieved over the ground, tussocks and stops and all — not the speed the legs think they are doing. This is trivial arithmetic and it is the single most common place a plan goes wrong, because the number people put into the denominator is so often an aspiration.

Now the honesty, and it is the whole point. Naismith assumed a fit walker, unladen, on decent ground, in daylight. Load, bog, navigation stops, a river crossing, tired legs and a gauge that will not reset all stretch the figure and none of them shrink it. Tranter's corrections are the standard extension when the estimate has to survive contact with a real hill. Treat Naismith as a floor: if the floor already runs past last light, no amount of pressing on will fix it.