How much time would pass between watching the sun set from ground level and then watching higher?

How much would time pass between watching the sun set from ground level and then watching it set again from the top of a sky scraper?

I heard once that this could be done using one of the towers of the World Trade Center. So I assume one could also do this using the Sears / Willis Tower in Chicago. Someone also told me that the world's tallest tower in Dubai is so huge that the local weather broadcast tells of two times for sunset. One time is for the observed sunset at ground level and another time is for the observed sunset from the observation deck near to the top of the tower.

unfortunately, I have recently gotten involved in a debate with someone who believes or claims to believe that the earth is flat and he has challenged me for proofs. I gave him some observations that any one can do, but that did not seem to be good enough for him. He wanted the mathematical predictions of an event and then a demonstration that showed that reality matches the mathematics.

Well, my math skills are a bit rusty on this sort of level since I have been out of college. Although I could probably do this, I figure it would be a greater ease for me to just ask one of the math majors or grad students that frequent online mathematics forums for the equations. So I think what I will do is list my ideas one at a time in this mathematical forum. And now, here is the first one.

The rapper B.O.B. has come out saying that he thinks the earth is flat. Neil Tyson gave him a reply and PBS offered an Op Ed piece explaining some simple tests anyone can do to prove the earth is round. One of them was to lay on the beach on your back and with your head pointed towards the sun set (do this on the pacific coast of course. The moment you see the sun set, immediately stand up and you can see the sun set again -- or so says the op ed piece from PBS. I have herd that something similar can be done with large buildings. If you watch the sun set on the ground level, (let's say from the point of view of a 6ft 4 man. Or some measured eye level from the ground) and then you take an elevator to the top floor, you will be able to see the sun set a second time.

The problem is this, if you know all of the variables, how long would it take to see the sun set a second time.

I hope I have posed this question well enough. Let me know if you have any questions. After this one is answered, I have at least one more question I will start in a second thread.