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How would you work out the precise times that the hands of ...

Sent to General Experts June 9 2006 at 10:02 AM
   

How would you work out the precise times that the hands of an analoge clock are over each other apart from 12pm assuming continuous mothion of both hands

 

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June 9 2006 at 11:41 AM (1 hour and 38 minutes and 50 seconds later)
         
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Okay, for finding out next time the hands are over each other, you use equation 5+5x=60x to get x=1/11. SO, the time is 1'oclock and 60/11 = 5 5/11 minutes, or 1:05 and 5/11 minutes (and to get seconds then multiply 60 and 5/11 to get 300/11 = 27 3/11 seconds, so it would be 1:05:27 and 3/11 seconds).

Next time, you would use 10+5x=60x to get x=10/55. SO the time would be 2'oclock
and ((60*10)/55 = 10 50/55 ) minutes, or 2:10 and ((60*50)/55) seconds = 2:10:54 & 30/55 second.

The next, (getting the idea?), 15+5x=60x, so x=15/55, so 3'oclock and ((60*15)/55 = 16 20/55 ) minutes, or 3:16 and ((60*20)/55 = 21 45/55 ) seconds, or 3:16:21 and 45/55 second.

The next, 20+5x=60x, so x=20/55. So the time is 4'0clock and ((60*20)/55 = 21 45/55) minutes, or 4:21 and ((60*45)/55 = 49 5/55 ) seconds, or 4:21:49 and 5/55 = 1/11 second.

The next, 25+5x=60x, so x=25/55. So, 5'oclock and
((60*25)/55 = 27 15/55) minutes, or 5:27 and ((60*15)/55 = 16 20/55) seconds. So its 5:27:16 and 20/55 second.

The next 30+5x=60x, so x=30/55. So the time is 6'oclock and ((60*30)/55 = 32 40/55) minutes, or 6:32 and ((60*40)/55 = 43 35/55 ) seconds, or 6:32:43 and 35/55 second.

The next 35+5x=60x, so x=35/55. So the time is 7'oclock and ((60*35)/55= 38 10/55) minutes. Or, 7:38 and ((60*10)/55 = 10 50/55) seconds. SO, it would be 7:38:10 and 50/55 second.

The next 40+5x=60x, so x=40/55. So the time is 8'oclock and ((60*40)/55 = 43 35/55 )minutes, or 8:43 and ((60*35)/55 = 38 10/55 ) seconds, or 8:43:38 and 10/55 second.

The next 45+5x=60x, so x=45/55. So the time is 9'oclock and ((60*45)/55 = 49 5/55) minutes, or 9:49 and ((60*5)/55 = 5 25/55) seconds, or 9:49:05 and 25/55 seconds.

And the last 50+5x=60x, so x=50/55. So the time is 10'oclock and ((60*50)/55 = 54 30/55 ) minutes, or 10:54 and ((60*30)/55 = 32 40/55) seconds, or 10:54:32 and 40/55 second.





Edited by jacket on June 9 2006 at 1:06 PM
jacket -- degree in math -- 100% Positive Feedback on 9 General Accepts
BS degree in math
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June 9 2006 at 1:34 PM (1 hour and 53 minutes and 7 seconds later)
         
Reply to jacket's Post: I would like to understand the equation and series, can you explain how you came to 5 + 5x = 60x, I guess each side describes the movement of a hand but I don't quite get it. 60x must be the hour hand?
Customer (name blocked for privacy)
Answer
June 9 2006 at 2:19 PM (44 minutes and 45 seconds later)
         
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Oh ok.
Well, actually 5x of the equation is for the hour hand.
The equation shows the relative speed between minute hand and hour hand.
As the minute hand goes around and moves 60x "spaces", the hour hand moves 5x "spaces".
And the 5 represent how far ahead the hour hand is from the minute hand, and this would be the case for 1'oclock.

So, x gives me how long , or how much of an hour it would take for the hands to land on each other!

Edited by jacket on June 9 2006 at 2:20 PM
jacket -- degree in math -- 100% Positive Feedback on 9 General Accepts
BS degree in math
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