How did you run the timer? Making turns in a battle? Just winging it?
They never knew exactly how much time was on the clock, only that a competing force was heading toward the same goal.
tl;dr: When they took actions that would increase or decrease their lead, I would give them a range of hours that it was likely to affect the other team.
Longer version: The near midnight in game-time, mission-giver told them that the competing team would leave at first light. Gave them a cart and horses and supplies and said, "If you leave now, you'll have up to a 6 hour head start. The more you push yourselves, the greater your lead will increase." They forewent a night's sleep that first night, kept their 6 hour lead. Tried it a 2nd night, and ended up
Exhausted. One of them had already been level-1 Exhausted before setting out, so she became 2nd-level Exhausted, and the other just 1st-level. But they'd gained another 6 hours or so.
Knowing they'd be screwed if they had to face challenges Exhausted and out of spells/abilities, they decided to rest once at an inn. After that, they kept pushing. They made it to the goal first, cleared the entire dungeon in three sessions, but due to IRL time running combat vs. in-game time, they only took a couple hours in-game to clear it.
If I were going to do it again, I'd use
Blades in the Dark Clocks for this, give them a four-segment Clock to have the competing team catch up, and a four- or six-segment Clock to chart progress toward the goal. Whichever one fills first, based on their actions and mistakes, would determine who makes it.