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# Clock

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873
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A broken clock is set corectly at 12:00 noon. However, it registers only 20 minutes for each hour. In how many hours will it again register the correct time  ?

A)12

B)18

C)24

D)30

E)36

i puted numbers and get 18 but i don t know how to make equation of these

Jan 16, 2016

#6
+40

A broken clock is set corectly at 12:00 noon. However, it registers only 20 minutes for each hour. In how many hours will it again register the correct time  ?

A)12

B)18  analog clock(12h)

C)24

D)30

E)36  digital clock (12h)

1. Analog Clock:

$$\begin{array}{rcll} \text{angular velocity real time: } \omega_1 &=& \frac{2\pi}{12\ h} \\ \text{angular velocity display time: } \omega_2 &=& \frac{2\pi}{36\ h} \\ w_2\cdot t - w_1\cdot t &=& n\cdot 2\pi \\ \frac{2\pi}{12\ h}\cdot t - \frac{2\pi}{36\ h}\cdot t &=& n\cdot 2\pi \qquad &| \qquad :2\pi \\ \frac{1}{12\ h}\cdot t - \frac{1}{36\ h}\cdot t &=& n \\ t\cdot (\frac{1}{12\ h} - \frac{1}{36\ h} ) &=& n \\ t\cdot ( \frac{36-12}{12\cdot 36} ) &=& n \\ t\cdot ( \frac{24}{12\cdot 36} ) &=& n \\ t\cdot ( \frac{2}{36} ) &=& n \\ t\cdot ( \frac{1}{18} ) &=& n \\ t &=& 18\cdot n \\ \end{array}$$

next correct time, if n = 1, then t = 18 hours.

2. Digital Clock(24h):

$$\begin{array}{rcll} \text{angular velocity real time: } \omega_1 &=& \frac{2\pi}{24\ h} \\ \text{angular velocity display time: } \omega_2 &=& \frac{2\pi}{72\ h} \\ w_2\cdot t - w_1\cdot t &=& n\cdot 2\pi \\ \frac{2\pi}{24 h}\cdot t - \frac{2\pi}{72\ h}\cdot t &=& n\cdot 2\pi \qquad &| \qquad :2\pi \\ \frac{1}{24\ h}\cdot t - \frac{1}{72\ h}\cdot t &=& n \\ t\cdot (\frac{1}{24\ h} - \frac{1}{72\ h} ) &=& n \\ t\cdot ( \frac{72-24}{24\cdot 72} ) &=& n \\ t\cdot ( \frac{48}{24\cdot 72} ) &=& n \\ t\cdot ( \frac{2}{72} ) &=& n \\ t\cdot ( \frac{1}{36} ) &=& n \\ t &=& 36\cdot n \\ \end{array}$$

next correct time, if n = 1, then t = 36 hours. Jan 19, 2016

#1
+10

I depends upon the type of clock that we are talking about.....

Note, Solveit.....every 3 hrs, it will  fall 2 hours behind....

In 6 hrs......it will be 4 hours behind

In 12 hrs.......it will be 8 hours behind

So....in 18 hours, it will be 12 hours behind.......and, as long as it's an analog clock....the clock's hands will appear to show the correct time, then !!!!

However.....if it's a digital clock......36 hours would have to elapse to show the correct hour......[ the digital clock would show AM or PM ]   Jan 16, 2016
edited by CPhill  Jan 16, 2016
edited by CPhill  Jan 16, 2016
edited by CPhill  Jan 16, 2016
edited by CPhill  Jan 16, 2016
#2
+10

There are 24 hours in a day and the clock is only going 1/3 the speed that it should

So in 24*3=72 hours

So we know that in 72 hours the clockes will be the same but will they be the same before that?

hour past Real time Display time
0 12 noon 12 noon
1 1pm 12:20
2 2pm 12:40

3 3pm 1pm
6 6pm 2pm
9 9pm 3pm
12 12midnight 4pm
15 3am 5
18 6morning 6afternoon
21 9 7
24 midday 8
27 3am 9
30 6 10
33 9 11
36 12 midnight 12 midnight
39 3 1

Ok so it is 36 hours.     Now I am trying to put this into a formula............

Jan 16, 2016
edited by Melody  Jan 16, 2016
#3
0

it is an analog clock

Jan 17, 2016
#4
0

Hi Solveit,

If you do not differentiate between AM and PM then obviously your answer of 18 hours is correct.

I am not sure about the formula either. :/

Jan 17, 2016
#5
+5

Ok Melody thank you and CPhill ! You can put a check mark :)

Jan 17, 2016
#6
+40

A broken clock is set corectly at 12:00 noon. However, it registers only 20 minutes for each hour. In how many hours will it again register the correct time  ?

A)12

B)18  analog clock(12h)

C)24

D)30

E)36  digital clock (12h)

1. Analog Clock:

$$\begin{array}{rcll} \text{angular velocity real time: } \omega_1 &=& \frac{2\pi}{12\ h} \\ \text{angular velocity display time: } \omega_2 &=& \frac{2\pi}{36\ h} \\ w_2\cdot t - w_1\cdot t &=& n\cdot 2\pi \\ \frac{2\pi}{12\ h}\cdot t - \frac{2\pi}{36\ h}\cdot t &=& n\cdot 2\pi \qquad &| \qquad :2\pi \\ \frac{1}{12\ h}\cdot t - \frac{1}{36\ h}\cdot t &=& n \\ t\cdot (\frac{1}{12\ h} - \frac{1}{36\ h} ) &=& n \\ t\cdot ( \frac{36-12}{12\cdot 36} ) &=& n \\ t\cdot ( \frac{24}{12\cdot 36} ) &=& n \\ t\cdot ( \frac{2}{36} ) &=& n \\ t\cdot ( \frac{1}{18} ) &=& n \\ t &=& 18\cdot n \\ \end{array}$$

next correct time, if n = 1, then t = 18 hours.

2. Digital Clock(24h):

$$\begin{array}{rcll} \text{angular velocity real time: } \omega_1 &=& \frac{2\pi}{24\ h} \\ \text{angular velocity display time: } \omega_2 &=& \frac{2\pi}{72\ h} \\ w_2\cdot t - w_1\cdot t &=& n\cdot 2\pi \\ \frac{2\pi}{24 h}\cdot t - \frac{2\pi}{72\ h}\cdot t &=& n\cdot 2\pi \qquad &| \qquad :2\pi \\ \frac{1}{24\ h}\cdot t - \frac{1}{72\ h}\cdot t &=& n \\ t\cdot (\frac{1}{24\ h} - \frac{1}{72\ h} ) &=& n \\ t\cdot ( \frac{72-24}{24\cdot 72} ) &=& n \\ t\cdot ( \frac{48}{24\cdot 72} ) &=& n \\ t\cdot ( \frac{2}{72} ) &=& n \\ t\cdot ( \frac{1}{36} ) &=& n \\ t &=& 36\cdot n \\ \end{array}$$

next correct time, if n = 1, then t = 36 hours. heureka Jan 19, 2016
#7
+10

Thanks Heureka ! :)

Jan 19, 2016
#8
+15

Thanks, heureka   !!!!   Jan 21, 2016