# Clock problem: Hour and minute hands interchanged

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Joined: Oct 12 2008 - 3:39pm
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Clock problem: Hour and minute hands interchanged

A man left his home at past 3:00 o'clock PM as indicated in his wall clock. Between two to three hours after, he returned home and noticed that the hands of the clock interchanged. At what time did he left his home?

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Joined: Feb 27 2013 - 3:54pm
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Re: Clock problem: Hour and minute hands interchanged

144/143((5*(3+3))+((3*5)/12)) minutes after 3:00PM
or 3:31.46853146853147..

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Joined: Oct 12 2008 - 3:39pm
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Re: Clock problem: Hour and minute hands interchanged

I am trying to decipher your solution but can't get through it. I hope you give time to explain how you get those numbers.. We have the same answer but mine is not so direct because I need a figure to formulate my equation. I hope you do share, thanks.

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Joined: Feb 27 2013 - 3:54pm
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Re: Clock problem: Hour and minute hands interchanged

yung ginamit ko po jan na method sir is yung naderive ko po based on some observations in solving parallel problems..

MD = (144/143)(MM+(MH/12))
MA = MH+(MD/12)

where,
MD = minutes of departure
MA = minutes of arrival
MH = minutes of the hour hand = 5*(kung anong oras) (e.g 10o'clock, MH=10*5=50)
MM = minutes of the minute hand

may two cases po sya:

case 1: if yung hour hand nauuna sa minute hand
case 2: if yung minute hand nauuna sa hour hand
*with respect po sa 12 o'clock mark clockwise direction

for case 1, MM = 5*(MH + greater hour)
for case 2, MM = 5*(MH + lesser hour)

yung lesser & greater hour is yung "after he returned ___ to ___ hours".

di ko po alam if may mali sa derivation ko..pero tama nman po so far sa mga sinolve kong problems :)

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Joined: Mar 2 2013 - 4:37am
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Re: Clock problem: Hour and minute hands interchanged

The columns a and b are constant
For column c, the first part is the time he left the home multiplied by 5.
The second part is the time he returned.

The solutions you will get for x is the time in minutes the man returned and for y the time he left his home. :)

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Joined: Oct 12 2008 - 3:39pm
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Re: Clock problem: Hour and minute hands interchanged

We have the same solution here. I found those equations with the aid of the figure. For the benefit of other readers, I uploaded my figure and formulate the equations you entered in the calculator.

→   Equation (1)

→   Equation (2)

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Joined: Jan 29 2013 - 2:45pm
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Re: Clock problem: Hour and minute hands interchanged

This is a nice thread =), it is very useful to student as well as for graduates who are about to take the board exam =) God Bless and more power. i'm looking forward seeing myself sharing =)

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Joined: Apr 12 2013 - 1:26pm
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Re: Clock problem: Hour and minute hands interchanged

sir pwedi p ba tayo maka post ng mga questions dito? di ko kaya sagotin ehh

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