"In 15 minutes" or "15 minutes later"?

Several years ago, when I was watching a show, it was 15:45 and the show started at 16:00. A foreigner asked me: "When will this show start?"

My English is not good, and I never talked to foreigners. I was very nervous then. I told him: "15 minutes later", but he seemed to not understand. So I thought it wasn't correct, and told him: "in 15 minutes". This time he understood.

I want to know if "in 15 minutes" is correct and "15 minutes later" is wrong under that condition? What's the difference between them?

Solution 1:

The phrase "in 15 minutes" is correct. It means after 15 minutes elapses, which is precisely when the show starts. The problem with "15 minutes later" is that it's not clear that it's relative to the present.

One show can start 15 minutes later than another, but if a show simply "starts 15 minutes later" -- later than what? The phrase "later" has to compare things such that one of them can be later than the other(s).