Question involving degrees: when will 2 hands overlap?

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iowateddy

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Here is my problem:
It is 3:00 p.m. on the clock. At what time (to the second) will the two hands of the clock overlap?

Please explain as simply as possible. I know that the hour hand moves 30 degrees in one hour and the minute hand moves 360 degrees in one hour. Why am I having trouble coming up with an equation?
Thanks,
Iowa teddy
 
Re: Question involving degrees

Here is my problem:
It is 3:00 p.m. on the clock. At what time (to the second) will the two hands of the clock overlap?

Please explain as simply as possible. I know that the hour hand moves 30 degrees in one hour and the minute hand moves 360 degrees in one hour. Why am I having trouble coming up with an equation?
Thanks,
Iowa teddy


The hour hand will move 360º in 12 hours or .5º/min.
The minute hand will move 360º in 60 min. or 6º/min.
For the minute hand to catch up with the hour hand, it will have to move 90+º plus some interval past 3.
The angle x through which the hour hand moves in this time period is .5N, where N is the total number of minutes from 3 P.M. to the time being sought.
The angle, 90 + x, through which the minute hand moves in this time period is 6N.
Solving for N and equating, we get x/.5 = (90 + x)/6 or 5.5x = 45 from which x = 8.1818º.
Since the minutes hand moves 6º/min. or (1/6)min/deg, 8.1818(1/6) = 1.3636 min = 1 min.-21.8sec.
Thus, the hour and minute hands will be coincident at 3:16:22.8 PM.
 
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