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What is the angle, in degrees, between the two hands of an analog Clock at 9:49? And at what EXACT time will the two hands be on top of each other? Thank you for help.

 Nov 16, 2018
edited by Guest  Nov 16, 2018
 #1
avatar+19697 
+2

The hour hand moves  360 degrees/(12 hours x 60 min)  degrees each minute= 0.5 degrees/min

    9 hours 49 min = 589 minutes     or 294.5 degrees

 

The minute hand moves  360degrees/60 min = 6 degrees / min

    49 minutes x 6 degrees/min = 294 degrees

 

294.5 - 294 = .5 degrees between the hands at 9 49

 Nov 16, 2018
edited by Guest  Nov 16, 2018
 #2
avatar+19697 
+2

The hands will be atop each other at what time?

 

 

270 + .5 x  = 6x      x = 270/5.5 = 49.0909090909090909        

                                                                    or 9:49 .090909*60 = 9:49:05.45454

 Nov 16, 2018
edited by Guest  Nov 16, 2018
edited by Guest  Nov 16, 2018
 #3
avatar+106515 
+2

At 9 o'clock......hands are separated by 1/4 * 360  =  90°

And, at this time.....let the minute hand be at 0°

And let the hour hand be at 270°

 

In 49 minutes.....the hour hand moves 360/12 * 49/60   = 24.5°

So.....the hour hand is at   [270 + 24.5]   =  294.5°

 

And the minute hand has moved  [ 0 +  49/ 60 * 360 ]  = 294°

 

So....they are separated by 0.5°  =  (1/2) of a degree

 

 

To find the exact time when they are together....

 

The hour hand moves at  30/60  =  .5 degrees per miniute = (1/2)° per minute

The minute hand moves at (360/60) = 6° per minute

 

So....we need to solve this

 

294.5 + (1/2)M  =  294 +(6)M       where M is the number of minutes sfter 9:49

 

Subtract 294 and (1/2)M from both sides

 

.5  =  5.5M      divide both sides by 5.5

 

.5 / 5.5  = M   =  5/55 =   1/11

 

So....they will be together 1/11 of a minute ater 9:49 ≈ 5.45 seconds after 9:49

 

 

cool cool cool

 Nov 16, 2018
edited by CPhill  Nov 16, 2018
 #4
avatar+4330 
+2

To answer the first problem, we can use the clock formula, which is \(|30H-5.5M|\). Therefore, plugging the values in, we yield with \(|30(9)-269.5|=270-269.5=\boxed{.5}\)

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 Nov 16, 2018
 #5
avatar+106515 
+1

Thanks, tertre!!!!

 

That IS easier to use.....!!!

 

 

cool cool cool

CPhill  Nov 16, 2018
 #6
avatar+4330 
+1

Welcome! This formula is pretty useful!

tertre  Nov 17, 2018

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