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 Post subject: Logic-TimePosted: Wed, 28 Sep 2011 15:06:54 UTC
 S.O.S. Oldtimer

Joined: Tue, 30 Dec 2008 20:37:56 UTC
Posts: 205
Location: Accra,Ghana
A clock loses 10 minutes each hour.
If the clock is set correctly at noon,

what time is it when it reads 3 PM?

I want to be able to make some meaning out of this question.How do I approach it?

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 Post subject: Re: Logic-TimePosted: Wed, 28 Sep 2011 15:49:23 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7949
Location: Lexington, MA
Hello, Kodwo!

An interesting problem . . .
It took a few tries to get an approach.

Quote:
A clock loses 10 minutes each hour.
If the clock is set correctly at noon, what time is it when it reads 3 PM?

Suppose we have two clocks: one which is accurate, the other loses 10 minute per hour.

Let = number of minutes the accurate clock moves.
Let = number of minutes the slower clock moves.

We know that: .

When the slower clock shows 3 PM, it has moved 180 minutes: .

. . Hence: .

The accurate clock has moved 216 minutes.
. . The time will be 3:36 PM.

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 Post subject: Re: Logic-TimePosted: Sun, 2 Oct 2011 18:03:30 UTC
 S.O.S. Oldtimer

Joined: Tue, 30 Dec 2008 20:37:56 UTC
Posts: 205
Location: Accra,Ghana
Thanks Soraban,

I have just been looking at the answer you supplied.

How did you get 5/6?

If the NOT accurate clock loses 10 minutes every hour between 12noon and 3pm( 3hours/180 minutes) it would have lost 30 minutes RIGHT?

I am lost and confused

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 Post subject: Re: Logic-TimePosted: Sun, 2 Oct 2011 18:45:13 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12098
Location: Austin, TX
Kodwo wrote:
Thanks Soraban,

I have just been looking at the answer you supplied.

How did you get 5/6?

If the NOT accurate clock loses 10 minutes every hour between 12noon and 3pm( 3hours/180 minutes) it would have lost 30 minutes RIGHT?

I am lost and confused

Remember it doesn't lose things all at once and it's asking what the REAL time will be when the BAD clock reads 3:00 pm.

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 Post subject: Re: Logic-TimePosted: Sun, 2 Oct 2011 19:18:12 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 23 Feb 2009 23:20:33 UTC
Posts: 1049
After 60 minutes have passed, the clock thinks that only 50 minutes have passed.

So clock time is 50/60 = 5/6 of real time.
Conversely, real time is 6/5 of clock time.

Thus at 3pm, the clock reads 2.30pm.
And at 3.36pm, the clock reads 3pm.

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 Post subject: Re: Logic-TimePosted: Sun, 2 Oct 2011 23:53:18 UTC
 S.O.S. Oldtimer

Joined: Tue, 30 Dec 2008 20:37:56 UTC
Posts: 205
Location: Accra,Ghana
Thanks everyone I got it now:

Let me try my hands on a similar question here:

A clock loses 15 minutes each hour. If the clock is set correctly at 1 pm, what time is it when it reads 5 pm?

Real Time = 3/4*Clock Time

Real Time = 3/4*240 minutes = 180 minutes

5:00 pm + 180 minutes = 8:00 pm

Hope I am right?

Thanks

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 Post subject: Re: Logic-TimePosted: Mon, 3 Oct 2011 00:30:43 UTC
 S.O.S. Oldtimer

Joined: Tue, 30 Dec 2008 20:37:56 UTC
Posts: 205
Location: Accra,Ghana
I corrected myself before anyone saw it

Real Time = 4/3*Clock Time

Real Time = 4/3*240 minutes = 320 minutes(5 hours 20 min)

1:00 pm + 320 minutes = 6:20 pm

Hope I am right?

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 Post subject: Re: Logic-TimePosted: Mon, 3 Oct 2011 01:34:48 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 23 Feb 2009 23:20:33 UTC
Posts: 1049
Kodwo wrote:
Real Time = 4/3*Clock Time

Real Time = 4/3*240 minutes = 320 minutes(5 hours 20 min)

1:00 pm + 320 minutes = 6:20 pm

That's correct.

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