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A certain clock marks every hour by striking a number of [#permalink]
25 Oct 2005, 12:31

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A certain clock marks every hour by striking a number of times equal to the hour, and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 22 seconds. At 12:00, how many seconds elapse between the beginning of the first sroke and the end of the last stroke?

Anyway, it's given that at 6 it takes 22 ticks. But we know 6:00 requires 6 chimes and 6-1 (N-1) gaps between chimes. And we know it's the same amt of time (say x) for both chimes and gaps. Which means:
6x + 5x = 22
=> x=2 secs

@12:00 it chimes 12 times with 12-1 (N-1) gaps.
The total chime time therefore= 12x + 11x = 23x = 23*2 = 46 secs

Calculating with 6 since we are counting from beginning of first stroke to ending of last stroke (and not the following interval), and since both time for the stroke and the time for the gap are the same then if x is the actual time of the stoke, [2(6) - 1 ]x = 22

which gives x = 2 sec.

So calculating for 12, the number of intervals with each being 2 second long are 2(12) - 1 = 23.