The original formula from classic was continual checks to see if you get ore, if it was in the rock. Later you could actually see the ore, but there was script for checking for getting ore more than once after metal pickaxes came along which allowed the player to have the game check sequentially. After RS2 came out, you mined until you got the ore and pickaxes were then an added bonus to be able to hit a successful ore gather. Fishing worked along those lines and so did woodcutting, except fishing never had equipment for multiple catching until RS2 allowed someone to fish until either they were full or the spot moved. I don't think the formula went from these gather checks to be given a time to gather, programmers reuse program script; the checks probably were made invisible. Adamantite ore, and runite, are some of the more painful ores to mine, sometimes taking 15 to 25 seconds to mine right at their respective levels, not because you are usually given a long time to be able to mine, it is because the programming makes it hard to hit a successful gather in the script.
There is more than formula in gathering, there's script, too. Iron mining was popular in 06 and beyond, because the programming at level 60 up with a rune pickaxe made most every mining swing an instant gather, not "oh, sorry, you hit a long mine attempt"