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Clock word problemIn this problem we will figure out all the times when the two hands...

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hellome234 | Salutatorian

Posted October 15, 2012 at 4:14 AM via web

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Clock word problem

In this problem we will figure out all the times when the two hands of a
clock are pointing in exactly the same direction and all of the times when
the two hands are exactly 180

apart.
a) According to a certain clock it is currently 2:16. At 2:16, the hour hand
of the clock is not pointing exactly at the 2, rather it is pointing at part way
between the 2 and the 3. Write decimals between 0 and 12 to express in hour
units exactly where each of the hands of the clock is pointing.
b) Suppose the current time is h:m o’clock. That is, it is m minutes after the
hour of h. So h is a whole number between 1 and 12, and m is a real number
between 0 and 60. Write decimals between 0 and 12 to express in hour units
exactly where each of the hands of the clock is pointing.
c) For particular values of h and m, when the time is h:m o’clock, the two
hands of the clock are pointing in exactly same direction. Write an equation
expressing m as a function of h.
d) Use each value of h between 1 and 12 to determine all of the times (up
to 2 decimal places) when both hands of a clock are pointing in exactly the
same direction.

 

Please answer part d

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2 Answers | Add Yours

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najm1947 | Elementary School Teacher | Valedictorian

Posted October 15, 2012 at 5:29 AM (Answer #1)

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The two hands are exactly in the same direction for a 12 hour clock only 12-1=11 times, hence interval between each such time = 12/11 hours = 1h+(60/11)m or 1h 05.4545m

d) All such times are:

1*(1h 05.4545m) = 01h 05.45m = 01:05.45

2*(1h 05.4545m) = 02h 10.91m = 02:10.91

3*(1h 05.4545m) = 03h 16.36m = 03:16.36

4*(1h 05.4545m) = 04h 21.82m = 04:21.82

5*(1h 05.4545m) = 05h 27.27m = 05:27.27

6*(1h 05.4545m) = 06h 32.73m = 06:32.73

7*(1h 05.4545m) = 07h 38.18m = 07:38.18

8*(1h 05.4545m) = 08h 43.64m = 08:43.64

9*(1h 05.4545m) = 09h 49.09m = 09:49.09

10*(1h 05.4545m) = 10h 54.55m = 10:54.55

11*(1h 05.4545m) = 11h 60.00m = 12:00.00

 

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selmasharafaz | College Teacher | (Level 3) Adjunct Educator

Posted September 18, 2013 at 3:52 PM (Answer #2)

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On finding part c, we can express m as a function of h, by the equation, 

m = h x 5.4545 or m = h x (60/11)

So, the times at which the two hands of the clock coincide and point towards the same direction are,

time = h + m , where m = h x (60/11)

or time = h + [h x (60/11)]

Therefore, the 12 times with value of h from 1 to 12 are,

h = 1 ; time = 1 h + [1 x (60/11)] m ; time = 01 h : 5.45 min

h = 2 ; time = 2 h + [2 x (60/11)] m ; time = 02 h : 10.91 min

h = 3 ; time = 3 h + [3 x (60/11)] m ; time = 03 h : 16.36 min

h = 4 ; time = 4 h + [4 x (60/11)] m ; time = 04 h : 21.82 min

h = 5 ; time = 5 h + [5 x (60/11)] m ; time = 05 h : 27.27 min

h = 6 ; time = 6 h + [6 x (60/11)] m ; time = 06 h : 32.73 min

h = 7 ; time = 7 h + [7 x (60/11)] m ; time = 07 h : 38.18 min

h = 8 ; time = 8 h + [8 x (60/11)] m ; time = 08 h : 43.64 min

h = 9 ; time = 9 h + [9 x (60/11)] m ; time = 09 h : 49.09 min

h = 10 ; time = 10 h + [10 x (60/11)] m ; time = 10 h : 54.55 min

h = 11 ; time = 11 h + [11 x (60/11)] m ; time = 12 h : 0.00 min

h = 12 ; time = 12 h + [12 x (60/11)] m ; time = 1 h : 5.45 min (the value is same as when h = 1 and the cycle continues)

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