Unless you have a system like some of the older d&d editions where it took ten minutes to "I search the room" ten minutes to "I search the chest he found for traps" & ten minutes for "I open the chest he found", it can be incredibly difficult to track because some things will take more & others less by a significant degree that players will find hard to predict
Luckily the players don't have to predict it, the DM (me) does.
Whether it is an established "system" like older editions, or me asking the player how long do they spend looking, or even a random die roll, it is all arbitrary really. I use general rules of thumb for many things like searching, movement, etc. As long as the time alloted is reasonable to everyone, the important part is tracking it.
I used to keep a tally sheet by hand, now I do it in Excel (but the same process) in minutes. 10 here, 3 there, an hour's rest, etc. accumulates and I announce when things happen accordingly. How granular I get depends on the activity and scene. In some cases, literally seconds will count... in others, minutes, or even hours are sufficient.
Well, like a torch burns for 1 hour. I usually just say, "Hey, it's been awhile so your torch is getting low. You better light another one." Then someone at the table will do the math real quickly and point out that our last six encounters only netted about 12 and a half minutes.
LOL I would ask them how they came to that time total then? If they sound right and you are happy with it, let them track time.
Otherwise, I often have found in the past when players do things like that there are often things they over look and/or under-estimate the time required to be reasonable to me (again, as DM, in particular).
AD&D, for example, have a very simple system when you consider encounters - 10 minutes (or a "turn"). After the rounds of battle, the excess time is binding wounds, catching breath, drinking some water, etc. Of course, rounds then were a minute long, not 6 seconds...
Movement, for example, is normal, quick (e.g. evading pursuit), or slow (ie. cautious). Given the "normal" speed 30 in 6 seconds, moving down a dungeon cooridor 60 feet long would not be just 12 seconds unless your PCs are just strolling like a day in the park! In most circumstances, PCs are exploring new terrain, perhaps keeping a simple map, etc. For each activity, I keep a mental tally of them all and multiple the time by that total.
For example:
The scout is 20-40 feet ahead of the point-man, who is 20-30 feet ahead of the party. The point-man's job is to keep an eye on BOTH groups, so has to keep pace to handle movement around a corner, or going up or down stairs, etc. Usually the scout has darkvision, so requires little or no light. The point-man might or might not have darkvision.
Each groups (scout, point-man, rest of party) moves and stops in coordination to be cautious, listening for sounds of enemies, looking for traps, etc. The tally racks up quickly, often resulting in the entire party moving only 5-15 feet (or less) per 6-second round.
Whenever an amount of distance is covered that is significant to the scene, I mark it off.
In outdoor settings the time frame adjusts, in towns or cities it adjusts, on horseback, or travelling with wagons, or whatever, it can change.
Yeah, I would like to purchase a supplement that explores this. One that Players and Dungeon Masters can use as a shared reference.
I would think there would be one out there someplace...