Let's think about this. If it's a quarter of an hour, that means it's 15 minutes into the hour. If the question were exactly 15 minutes after the hour, it would be 60 minutes total, because in between the two is exactly an hour. But since it's asking for 14 minutes after the hour, it's one minute less than 15 minutes after the hour, so it should be 60 - 1, or 59 minutes.
