D&D 5E How to Run Combats in a Cavernous Dungeon Without Alerting All NPC's?

[FitzTheRuke]

My dialogue might have made them sound a bit stupid, probably because I meant it a bit tongue-in-cheek, but trust me, even a group of very smart people can needlessly bicker before collectively acting. A single giant would probably act faster than a group (in particular if they're on duty or on patrol). But unless that group is actively standing at attention, waiting for trouble, they're likely to discuss the event before acting. Unless there is a clear leader, and that clear leader is the one who understood what is going on the best.

But yes, a random number before they ACT, and then calculate movement. Or calculate rough-approximate movement ahead of time, and simply add it to the random roll, to come up with their arrival time.