How soon will the hands of the clock be together again?

[NEHA]

How soon after noon will the hands of the clock be together again?

I realize that the hands will be together after 12 hours, of course. But are they asking for a time sooner than midnight, when the hands overlap again?

 

[TchrWill]

how soon after noon will the hands of the clock be together again?
after 12 hours ofcourse...
or are they askingfor when will the hands reach noon once again?

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 again, it will have to move 360º plus some interval from 12 past 1.

The angle x through which the hour hand moves in this time period is .5N, where N is the total number of minutes from 12N to the time being sought.

The angle 360 + x, through which the minute hand moves in this time period is 6N.
Solving for N and equating, we get x/.5 = (360 + x)/6 or 5.5x = 180 from which x = 32.727272 degrees.

Since the minutes hand moves 6º/min. or (1/6)min/deg, 32.727272deg = 32.727272(1/6) = 5.454545 min = 5 min.-27.27sec.

Thus, the hour and minute hands will again be coincident at 1:05:27.27 PM.

 

[NEHA]

wowwwwwwwwwwwwwww that was a long procedure
i could of never gotten that answer in my whole life. thank you so very much

 

[stapel]

How soon after noon will the hands of the clock be together again?

Since the minute hand must make a full revolution every hour, and since the hour hand only moves 1/12 of the way around the face of the clock, then it is immediately obvious that the hands must overlap again sometime shortly after 1pm:

The minute hand will start and end at "12", but the hour hand will move only from "1" to "2". A quick estimate in your head should indicate to you that the hands will overlap at between 1:05 and 1:10.

Eliz.