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What is the first time after 1pm at which the minute hand and hour hand of a clock point in exactly opposite directions?

 

Hint: 147

 

thank u guys in advance :)) also, i don't know what the hint means :(

 Jun 7, 2020
 #1
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I think you mean when they are 180 degrees apart:

 

180=abs((30*1) - (5.5*M)), solve for M

 

M =420 / 11 =38.181818........minutes - or 38 minutes and about 11 seconds after 1 O'clock.

 Jun 7, 2020
 #4
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thank you guest!!

andrewstanells  Jun 8, 2020
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Just thinking about it logically I can see that this will happen between 1:35 and 1:40 So any calc I do can be checked against this.

 

The hour hand starts 30 degrees past the hour and the minute hand starts on the hour.

 

After 1 minute the hour hand travels 0.5 degrees and the minute hand travels 6 degrees

so

After x minute the hour hand travels 0.5x degrees and the minute hand travels 6x degrees

 

the hour hand starts on the 1 so it has that 30 degrees 'head start'

 

The angle between for the first half hour of so will be  6x-(30+0.5x) and we want that equal to 180

 

Solve the equation and we get x= \(38\frac{2}{11}\;\;minutes\)

 

So at   \(38\frac{2}{11}\;\;minutes\)  past 1 the hands will be exactly opposite each other.

 

(just as our guest already determined. - thanks guest)

 

 

 

 

 Jun 8, 2020
 #3
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thank you!! that helped a lot :))

andrewstanells  Jun 8, 2020

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