In New Zealand the common practice is to use time as the measure of distance between two points, and most signs will indicate time. DOC (Department of Conservation) Government organistation responsible for looking after National Parks etc. have more recently been putting distances on signs along with times, which gives you a good idea of what to expect of the track ahead (it is quite common to see the km equal the hours, and you know you are in for for a tough workout).
One reason would be that tracks and routes historically(outside the really popular track such as the "Great Walks") have never been measured accurately, and prior to GPS quite difficult to get a reasonable distance measure. And as Roger pointed out, most people just want to know if there is enough time to get to the next destination or not, or just how long is the suffering going to continue.
One thing with stated times in New Zealand to be aware of is if the track is close to a roadend and is suitable for family groups then walking time of a medium fitness party would be less than stated by a quarter to a third. Standard tramping tracks have times quoted that medium fitness parties would normally match. In more remote regions with minimal routes or straight wilderness, quoted times would match those of a fit experienced party but also would be somewhat variable due to conditions such as snow, mud, rain, wind, and most likely reason route finding.
Beating quoted times is considered a mildly entertaining diversion to the serious nature of tramping, and a method of getting one up on someone. ;-)