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math question: OG math, green book

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math question: OG math, green book

by semidevil » Sat Jan 03, 2009 10:30 am
Im looking at problem 110 from the OG math green book:

"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, the time lapes between the beginning of the stroke and the end of the last strokee is 22 seconds. At 12, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?"

First of all, I'm not even understanding the problem. Can someone explain to me simpler terms?

A certain clock marks every hour by striking a number of times equal to the hour

So if it is 6 oclock, it will strike 6 times?

and the time required for a stroke is exactly equal to the time interval between strokes

what?

At 6, the time lapes between the beginning of the stroke and the end of the last strokee is 22 seconds

so it takes 22 seconds to strike 6 times at 6 oclocks?

the question asks:



At 12, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?"

I'm not understanding the question and how to logically relate the information.

tips?
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by DavoodBeater » Sat Jan 03, 2009 12:43 pm
in order of your questions:
- yes
- the time that you hear the sound is the same as the time you dont hear (silence between strikes)
- exactly, also you can say from first "ding" to the end of the last "ding"
- questions asks this time for 12 o'clock.

so:

just count: first strike + first silent + second ...+ 6th strike
so 2 sec for "ding" and 2 sec for silent
(you must not add last silent)
therefore the answer is 46.

tip: 6*2*X - X=22 => X=2
12*2*2 - 2=46
clear?
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by logitech » Sat Jan 03, 2009 4:58 pm
I will never understand this question :(
LGTCH
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by rajataga » Sun Jan 04, 2009 10:16 am
Yup, it's 46...

To explain this, semidevil try to imagine those grandfather clocks....

the problem just says that the clock signifies every hour, by sounding a number of times which is equal to the hour it is....

now, if it is 4 p.m., the clock will sound 4 times. and in between each of these sounds, there will be a break, the duration of which will be equal to the duration of the sound.

However, it is important to note that the number of breaks between the sounds, will be 1 less than the number of sounds itself.

Hence, when the clock sounds 6 times, there are 5 breaks between them...

so, if x = duration of the sound/break ( they are the same)

Hence, 11x = 22

hence, x =2

Now, for 12 pm/am

there will be 12 sounds, which will be separated by 11 breaks, hence,

(12 + 11) X 2 = 46secs
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by nervesofsteel » Tue Jan 06, 2009 12:35 am
DavoodBeater wrote:in order of your questions:
- yes
- the time that you hear the sound is the same as the time you dont hear (silence between strikes)
- exactly, also you can say from first "ding" to the end of the last "ding"
- questions asks this time for 12 o'clock.

so:

just count: first strike + first silent + second ...+ 6th strike
so 2 sec for "ding" and 2 sec for silent
(you must not add last silent)
therefore the answer is 46.

tip: 6*2*X - X=22 => X=2
12*2*2 - 2=46
clear?

Thanks for the explanation
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