That was funny considering both the transporter room and sickbay are on lower decks.
I'm not so sure about the transporter room. In Star Trek 2009
, could Chekov made it there while Kirk and Sulu fell if he had to stop and take a turbolift?
Look at SFS ... in the span of what we're supposed to believe is 60 seconds, Kirk & co leave the bridge, take an elevator ride, run down a hallway, get to the transporter, beam out ... and then there is still time for klingons to beam aboard, go back up to the bridge, and look around, before the thing blows.
Makes the last 16 seconds till detonation in DOOMSDAY MACHINE (which is more like 2min) seem HIGH NOON-accurate with respect to screen time.