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A certain clock marks every hour by striking a number of

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A certain clock marks every hour by striking a number of [#permalink] New post 28 Mar 2006, 17:10
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A certain clock marks every hour by striking a number of time 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 the 12:00, how many seconds elapse between th beginning of the first stroke and the end of the last stroke?

A. 72
B. 50
C. 48
D. 46
E. 44
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Re: PS -110 from OG work Quan workbook [#permalink] New post 28 Mar 2006, 17:40
46.

At 6, there are 6 strokes and there are 5 intervals between strokes.
Let t = time required for a stroke = time interval between strokes.
Thus, the 6t + 5t = 22 => t =2.

At 12, 12 strokes and 11 intervals => 12t + 11t = 23t = 23(2) -46.


myc2004 wrote:
A certain clock marks every hour by striking a number of time 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 the 12:00, how many seconds elapse between th beginning of the first stroke and the end of the last stroke?

A. 72
B. 50
C. 48
D. 46
E. 44
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 [#permalink] New post 31 Mar 2006, 10:21
time between strokes = time of each stroke

6 pm --> 6 strokes

Stroke 1 -> n seconds
n seconds between stroke 1 and 2
Stroke 2 -> n seconds
n seconds between stroke 2 and 3
Stroke 3 -> n seconds
n seconds between stroke 3 and 4
Stroke 4 -> n seconds
n seconds between stroke 4 and 5
Stroke 5 -> n seconds
n seconds between stroke 5 and 6
Stroke 6 -> n seconds

Total: 11 n seconds = 22 seconds, n = 2

12 -> 12 strokes + 11 in-betweens. Number of seconds = 12n + 11n = 23n = 46 seconds
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 [#permalink] New post 31 Mar 2006, 16:44
If d is the duration of the stroke == duration of the pause between stroke. The total duration (start to end) at every hour :

(2n -1 )d = Total Duration

where n is the hour.

At 6:

(2x6 -1) d = 22

Therefore, d=2

So when n ==12

(2x12 -1)2 = 23 x 2 = 46
  [#permalink] 31 Mar 2006, 16:44
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