Seconds of a Clock

Question

A clock takes 12 seconds to strike 4, how long does it take to strike 12? I have already tried EVERYTHING, but nothing seems to work.

Answer 1

If it takes a clock 12 seconds to strike 4, then it will take another 12 seconds to strike 8 and another 12 seconds to finally strike 12. Adding these together, we get either 36 seconds total or 24 seconds after striking 4.

Answer 2

HINT: The time taken to strike $4$ is essentially all accounted for by the $3$ intervals between the strokes. When the clock strikes $12$, there a $11$ of those intervals. Assuming that all of the intervals are the same length, how much time will those $11$ intervals require?

Answer 3

This is a bad question. An assumption is needed to solve it with the given info.

A single strike of the clock can be visualised as the sum of a "chime" ($C$) and a "gap" ($G$). The total length of a strike is therefore $C+G$.

$4$ strikes would be depicted as: $CGCGCGC$, the last gap being ignored as the timekeeping would stop once the final note has died off.

We can therefore state: $4C + 3G = 12$.

We are now asked to find how long $12$ strikes would take, and that's $12C + 11G$. The problem is that we have insufficient information to make that determination. If we had information on $8$ strikes (say), we could solve a pair of simultaneous equations and accurately state how long $12$ strikes would take.

However, as things stand, a simplifying assumption of $C \ll G$ needs to be made. This allows us to completely neglect the $C$ terms and say $3G = 12$, hence $G=4$ and get $11G = 44$ ($44$ seconds for $12$ strikes) as the answer.

My issue is: is that assumption justified? In my experience with large clocks (grandfather clocks, clock towers, etc.), the chime definitely takes a finite interval that is non-negligible relative to the gap.

So I conclude: this is a bad, bad problem.