There is the puzzle that given the information that:
a clock at 6 o'clock struck 6 times and the time elapsed between the first and last strike was 30 seconds asks how long will it take to strike 12 times at noon.
The first and intuitive thought is to use average i.e. 30/6 * 12 = 60 seconds. But that is wrong.
Although I do know the answer, which is that we need to distinguish between the strikes and the breaks I am not sure how to formalize it in the sense with what is this comparable that we are familiar with.
I mean if we were given instead of clock strikes e.g. prepare cakes I think the first thought again would be the average per cake but I am trying to understand where the fallacy comes from and what is the formal way to remove it (with something else we are familiar).
Update: In regards to the prepare cakes example that confused people. What I meant was that following 2 puzzles are directly equivalent:
a clock at 6 o'clock struck 6 times and the time elapsed between the first and last strike was 30 seconds asks how long will it take to strike 12 times at noon.
a cake is hand out to a customer/waiter at min 0 and the 6th cake is handed out in min 30. How long will it take to hand out 12 cakes?
What I had in mind is that there seems to me that there is a more general process that is directly there for both clock/cake puzzle and as a result we would make the same fallacy i.e. for the cakes 30/6 * 12 = 60 mins which should be wrong since again the preparing of the cake (which is the equivalent of the break between strikes) is still not taken into account.
Of course I might be confused completely and would be glad if my confusion was cleared by someone