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Find the earliest time after 3 PM that the hour hand and minute hand of a clock overlap.  Give your answer with an exact number of minutes.

 May 4, 2020
 #1
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+1

0=abs((30*3) - (5.5*M)), solve for M

 

M =180 / 11 =16.36363636.....etc. =16 minutes and about 22 seconds after 3 PM

 May 4, 2020
 #2
avatar+111326 
+1

Let tthe top of the clock  =  0°

At 3 PM  the minute hand will be at  this position

And  the hour hand will be at 90°

The minute hand  moves at 6° per minute

The hour hand moves at   .5°  per minute

 

So  when they overlap  the  distance they are from the top of the clock will be the same..so....using  rate * tme  = distance we have that

 

6T   = 90 + (.5)T    subtract .5T  from both sides

 

5.5 T  = 90          divide  both sides by 55

 

T  ≈  16.36  min after 3 PM

 

 

cool cool cool

 May 4, 2020

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