A certain clock marks every hour by striking a number of times equal to the hour and the time required a stroke is exactly equal to the time interval between the strokes. At 6 the time elapse between the begining of the first stroke and teh end fo the last stroke is 22 sec. At 12, how many seconds elaspse between the beginning of first stroke and the end of the last stroke?

A 72
B 50
C 48
D 46
E 44


Can you please "mathematicize" the underlined and show the setup and the answer for this question? I am not satisfied with OG's explanation.

Thank you

At 6, the clock strikes 6 times. Also, there are ONLY 5 intervals between the strokes. Since the time for stroke and time between intervals is the same, we have 11n = 22 (n is the time for each stroke)
n = 2

At 12, the clock would strike 12 times and there are 11 intervals. So, (12+11)*2 = 46

Nice explanation by the Guest. When you get something like this and it is confusing you (as this one certainly would!) try and literally picture it. You're standing in front of a big grandfather clock - and actually play out in your mind what it means to have, at 6, a number of strikes equal to the hour, and then intervals between the strokes (count them up - for 6, there are 5 intervals, as the 2nd poster said). And then just think - if it takes one second to strike, then it also takes one second between strikes. Try to make it as real as possible.

Then, you can go ahead and set up the math, as the Guest poster did.