How do you keep track of the time the party spends exploring a dungeon or area (outside of combat)? I have a wizard in my party who likes to cast Detect Magic while exploring, which lasts for 10 minutes. I am trying to figure out a fair method by which to determine how long the party has been exploring so that I know when that effect (and others) will end. 

The first solution that seems obvious is to simply keep an active timer running and tell the party that they are exploring in real time. This seems fair and would encourage quick thinking and planning ahead, but comes with one major issue. I can only cover one person's actions at a time. So two party members might doing two different things at the same moment in time, but I have to cover them individually(thus taking up more time than it would actually take the party to complete these actions).

The second solution could be to take initiative and give each player a turn to explore, using the 6 second rule from combat, but I do not want to do this as it seems clunky and would only make exploration feel more tedious.

Are there any other clever ways you have come up with to track time spent exploring that seems fair to the party? 

"RPGs where a three weeks journey takes 5 minutes and a three minute combat takes 4 hours."  
Joking aside, in the case of your wizard, I would calculate the movement speed and adjust for careful investigation / exploration.  That will give you a rough idea of how much territory can be covered during the spell duration.  Then, just let the player know when they are nearing the limit.  Since that character is concentrating on the spell, they should have a feel for its  duration.

Quote from Eriniel >>

"I would calculate the movement speed and adjust for careful investigation / exploration.  That will give you a rough idea of how much territory can be covered during the spell duration."

 I feel that this is easier said than done. Taking into account other group members and what they are doing, the pace they move at may change at any given instant. Plus, there is no guarantee that the player will spend the same time carefully investigating one area compared to another, especially if there is a stark difference in size and detail to the areas they are exploring. 

I feel that trying to estimate times this way introduces too many variables. I also fear that trying to use estimates for how long they would spend doing a particular activity, with the variations that can occur, leave room for debate between the player and I for how we each would estimate it and then time is wasted coming to an agreement. 

The short answer is you decide. 

From SRD.

"In situations where keeping track of the Passage of time is important, the GM determines the time a task requires. The GM might use a different time scale depending on the context of the situation at hand. In a dungeon Environment, the adventurers’ Movement happens on a scale of minutes. It takes them about a minute to creep down a long hallway, another minute to check for traps on the door at the end of the hall, and a good ten minutes to Search The Chamber beyond for anything interesting or valuable."

Different tasks take different amounts of time. If there's not a lot happening and the party isn't doing a lot of checks or searching for secret doors, etc then time can pass quickly. There's no need to track each step or movement. If you have a player who is determined to search every inch of a wall then that could take several minutes.

Personally, I think you're opening a can of worms trying to track it so precisely. You don't need to overthink it. Just say "That took about 3 minutes." or say "Your Detect Magic is about to drop" 

You need to ask the players how carefully they're investigating. If they just walk into a room and look around, then I would say 30ft every 2 turns. 1 turn to move, 1 turn to look. But it's not really investigating, is it. Are they going to be flipping beds, lifting rugs, patting down the wall for hidden nooks and crannies? That would be more like 5ft per turn. If that. But the longer they look, the lower your DC would get for finding stuff. So you could easily use the 5ft sqr per turn and multiply it by all occupied squares on your map, or a sqr adjacent to a wall. Don't include empty squares in the middle of the room, because you can't really investigate that.

SO! Now you have a party that is intensely combing over a 20x20 room with a bed that is 4sqr and a dresser that is 2. That works out to be 86 turns. Divide that by the number of searchers. Say a party of 4. 21turns, more or less. Bear in mind, this is just about searching/investigating, not about detect magic, which makes stuff glow. If you're just wandering around looking for a magical aura, you would move much quicker.

" If they just walk into a room and look around, then I would say 30ft every 2 turns. 1 turn to move, 1 turn to look. But it's not really investigating, is it. Are they going to be flipping beds, lifting rugs, patting down the wall for hidden nooks and crannies? That would be more like 5ft per turn. If that."

Not that I would disagree with using this out of combat to make it more interesting but it's not RAW.

Assuming average movement is 30' then moving, and then spending a round rolling for Investigation, that makes sense. 2 turns to move and search. (In terms of combat movement) But to then say out of combat it would take longer to search for hidden nooks and crannies doesn't make sense. 

Unless the player says something like "I want to spend a full 2 minutes looking through this stuff" there's no reason it should take a different amount of time out of combat.

I appreciate the feedback so far. The main thing I am looking for is a way to manage it WITHOUT needing to micromanage and determine the timing on every single activity. Up until now, I have been doing it as BTI_Brian said and just state "your Detect Magic is about to drop." I was mainly hoping to find a way to better estimate how much time has passed that isnt quite so "up in the air" but also isnt strict micromanaging. Its a strange middle ground to find, I know

In the particular case of detect magic, you can just figure it doubles the amount of time it takes to do a search, since it takes 10 minutes to cast ritually and lasts for 10 minutes.