Without using a calculator, the internet, or other mechanical assistant, how would you answer the poll question?
I would say:
12 times faster, as the hour hand sweeps out one segment in the same time it takes the minute hand to sweep out 12 segments
12 times. It takes the hour hand 12 hours to do the circle, the minute hand takes 1 hour.
Yeah, it’s obvious to me. I used this as an example of real world math everyone should be able to get right. Others disagreed, saying some people (who are otherwise clever) just don’t know have any mathematical sense.
The posters around here are generally a good proxy for smart people. I’m curious how many genuinely get it wrong.
3,600
It takes 12 hours for the hour hand to complete a revolution, that’s 3,600 minutes
I did have to do some thinking but I got it right. Nice question, tho 
Digital clock! Down with hands!
Up with mini-skirts!
I almost fell into the “sixty times” trap, but paused to visualize it first.
This is why God created Public Polls, btw. So we can ceaselessly mock those who provided wrong answers. 
I refuse to accept that “how fast” here means the number of rotations per time unit rather than the distance tracked by the tip of the hand per time unit. The answer is therefore undetermined unless the relative length of the hands is specified - the minute hand moves 12*(minute hand length/hour hand length) times faster than the hour hand. Also, there are 24-hour analog clocks where the correct answer is 24 rather than 12.
There is another question that is not so simple to answer or explain. How many times a day does the minute hand pass the hour hand?
I dislike the expression “times faster” and prefer “times as fast”. In my view, “12 times as fast” = “11 times faster”.
I do not expect to win a prize for this opinion.
I’d like you to go back and and read the first part of that sentence aloud to yourself.
Are you saying it does not take 12 hours for the hour hand to make a complete revolution?
Duh…I fell into the trap.
But to answer your question, assuming you mean day as 24 hours and not diurnal, it’s 24. (Technically the possible special case of 25 times doesn’t quite happen even if you start at the exact second.)
Yes, the hour hand does take 12 hours to make a complete revolution. But since the minute hand makes 12 revolutions in the time the hour hand makes one, it is impossible for it to be 3600 times faster. The minute hand makes 12 revolutions to the hour hand’s one, so that’s a 12:1 ratio.
I didn’t consider this. Both RPM and MPH are valid measurements of speed so the RPM answers aren’t wrong, but not the only possible answers.
Ah, I’m thinking of the second hand
Still, the second hand makes only 720 revolutions in 12 hours.