How to calculate in-world time needed to complete quests?

Question

Similar to my other question: How to handle parallel timelines when your party is separated?

but both party is racing to finish their task. There is a bet on which party found the flower and bringing it back to the guild first. This is not my intention, but decided among themselves.

Because the challenges on both regions are different, I find it will be hard to calculate the time spent by each party fairly.

Region A: Traps and checks, mainly Survival and Nature, to recognize the correct flower.
Region B: 3 encounters (normal enemies), fairly straightforward location.

How to calculate how long time has elapsed for each region?

I'm aware of this question: How to handle time in D&D 5e, but it doesn't account for the time needed to travel when searching for the flower in region A, and to calculate the time of combat in region B.

Answer 1

There are no strict rules for precise time calculation

Unfortunately, "two PC teams racing" simulations doesn't work well in 5e. There are rules on precise tracking time for particular situations (like combat rounds or travelling pace), but in most situations a DM is supposed to measure time roughly. That will be subjective, hence, might not feel "fair".

Time is just another kind of resource, available to PCs

The point of any time restrictions in 5e adventures is not to make players racing each other. Variety of resources can give players opportunities to make meaningful decisions. For instance, a wizard can cast Leomund's Tiny Hut as ritual or he can save ten minutes but spend a spell slot. A rogue can search for traps thoroughly, but spend a couple more hours, or she can take the risks, probably lose some HP triggering the trap. Players can spend more time sleeping, searching for food and water, or they get one more level of exhaustion, etc.

Sometimes the rules give you precise timings (like +10 minutes when you perform a ritual), but in most cases the timings are up to the DM. The rules generally don't specify precise timings for task resolving, since a single skill check might mean very different things (a momentary decision was made, or the whole day was spent searching).

What to do?

So how can you resolve the situation? I suggest you not to focus on the precise time management, but make the game more fun to play. D&D rules is not a reality simulator. You won't achieve "fairness" by following the rules as literally as you can. To make the game feel "fair", let your players have agency. Let them make meaningful decisions. Let them face the consequences. When time matters - give them an opportunity to save more time by sacrificing other resources, or by making clever moves. Let them be creative.

Visualize the game time - draw a clock, or use counters - set a deadline, and give your players opportunities to save (or spend!) more time. Every saved hour must have a cost. An example:

— We decided not to sleep and spend 8 more hours for searching for the flower.
— That will probably be all-consuming. I'll ask anyone for the Constitution check (DC 15) and give one level of Exhaustion on fail. Do you do that?

Another example:

— I'm searching for a large beast footprints.
— Okay, make a Survival check, with disadvantage, because it's already too dark to see clearly. You can wait for tomorrow though.
— No, I don't want to wait. I can use a torch, or cast Light, can't I?
— You can indeed, but it probably lures more stirges to this place. Do you do that?

Answer 2

Turn both regions into dungeons and count rounds

If you really want to keep strict count of time, the built-in way to do that is to count rounds, in intervals of 6 seconds. When I've done dungeon crawls, I have had long stretches where we were keeping track of turn order and using round-based movement/actions even outside of combat. You can use this method to accurately keep track of time by counting the total number of rounds that have elapsed.

In order to do this, both of the paths need to be "dungeons," and particularly dense ones at that--there needs to be some obstacle or encounter that the PCs need to address every round. These can take the form of hostile creatures, or traps, or some other time-based threat. Otherwise, you run into the problem of entire rounds spend simply walking, which is tedious for everyone involved.

Alternatively, take inspiration from the D&D Championship

There used to be D&D tournaments, in which teams of players would compete with other teams, under strict time limits and had scoring systems.

Unfortunately, I can't seem to find specific details of the scoring system or the tournament versions of adventures played (though the Hidden Shrine of Tamoachan is frequently mentioned). However, there are a few firsthand accounts:

This year’s Championship was an adventure called A Hole in the World. Five level 25 pre-generated PCs, were provided. Each team had to complete five encounters, each encounter with a 45-minute time limit. If you didn’t complete an encounter in 45 minutes you were eliminated. If the party decided to take an extended rest you were eliminated. It was designed to challenge the best and most experienced D&D players and it certainly did just that.

In previous years, all teams participating in the D&D Championship were scored based on a number of different criteria. You gained points for the number of encounters you completed and the number of PCs who survive.

You probably don't want to replicate the tournament setting exactly, but you could set real-world time limits and a scoring system in order to adjudicate this competition between your players.