The “That’ll be a DC 15 check and take 10 minutes” bit? I mean, those words are pretty close to something I would say when running a game, but I can’t tell if it accurately reflects the gameplay at my table because the surrounding context is missing.
Then can you explain the context better? The PCs have identified an obstacle, as DM you're telling them what is required to overcome that obstacle and how long it will take. In the case you mentioned it was a trap, I've given examples of a lock.
I think the lock example is a little simpler if that's okay as a start. I don't want to get into specific verbiage of how skills are involved, that's pretty secondary. So a slightly abbreviated encounter might look something like ...
DM: The door has a padlock on it.
Joe: I take a closer look, is it trapped?
DM: Make an investigation check
Joe: 15
DM: As far as you can tell there are no traps, do you you attempt to open it? [DM knows it's a DC 20]
Joe: Yep, I get a 17.
DM: It's apparently more difficult than it looks It doesn't open, you can keep at it but if it doesn't open right away it could take a few minutes, even up to half an hour.
Joe: Okay, I'll try again for a few minutes.
DM: [Rolls in secret, gets a low number meaning it's going to take a while.] You've tried for about 5 minutes, how much longer do you want to try?
Joe: Ugh, tough lock. We haven't seen a patrol yet [there is no immediate time concern, but some] so I'll try up to half an hour.
So I never told the PC exact numbers, just generalities. I might have variations on this but that's the gist. There may even be situations where the 15 investigation wasn't high enough to find an alarm trap and the padlock
can't be opened even after half an hour (in world time, not game time) in which case either guards will have shown up or I'd say something about the lock being broken.
FYI: I have a game and won't get back to this for a while.