I don't think anyone will really miss much time at any port of call. In the first place, the captain can increase his speed by just a few knots and make up a considerable amount of time. If that doesn't make up the time, shorting each port by less than an hour should solve that problem. On the subject of the medical emergency, I've seen several medical emergencies where someone had to be removed from the ship and I can't recall a time when the task wasn't accomplished within an hour or so. I can't imagine what kind of medical emergency would take that much time.