After exactly 12 o' clock noon, what time will the hands of a clock be together again?

Question

This is a word problem of Mathematics

Answer 1

In reality the motion of the hands of a clock are not instantaneous, but continuous.

Let x = time, y = position on the clock
The hour hand is defined by
y = x/60
The minute hand is defined by
y = x/5, (x-60)/5, (x-120)/5 etc
We are interested in the intersection between
x / 60 = (x - 60*n) / 5
11/60 * x = 12*n
x = 720*n / 11

For n = 1, x = 65 5/11
That corresponds to 1:05:27

The other times are:
2:10:55
3:16:22
4:21:49
5:27:16
6:32:44
7:38:11
8:43:38
9:49:05
10:54:33
12:00:00

Answer 2

It is not exactly well worded to be a word problem. Here's why, a clock's precision of movement is dependent of it's mechanism, hence the increment at which the hour, minute and second hands move is directly related to each other. Now in order to calculate the time interval, you need the increment. Here it is more graphically: Every hour the minute hand passes over the hour hand 'at some point', but if the hour hand's movement is dependent exclusively on the minute hand, then each minute, the minute hand moves 6 degrees, while the hour hand moves .5 degrees, so that means that the only time when the hands are exactly over each other is at 12 hour intervals after 12 o'clock; but that is not an answer either. . . see where I'm getting at? You need an interval that is exact to the second, but that won't do it either because you'll end up with fractions of a second. . . If you are talking about a theoretical clock with infinite precision, then at a period of every 1 hour 5 minutes and 5/11 seconds the minute hand will pass over the hour hand. which gives you a recurring decimal so that is no good either. . .

Answer 3

Because the hour hand will also move slightly past the hour as the minute hand makes a revolution around the clock...
1:05.5, 2:11, 3:16.5, 4:21, 5:26.5,,..
add 5 minutes 30 seconds to each hour to more closely approximate the hands being together each rotation of the minute hand.

Answer 4

The hands will be together again when both hands touch the same number. So for example, the next time they will touch the same spot will be 1:05 p.m. The next will be 2:10 p.m. & so on.

Answer 5

Depending on the type of movement: 1:05, or 1:05 1/2, or 1:06.

Answer 6

Hi!.
he hands of a clock be together again at,
1.05
2.10
3.15
4.20
5.25
6.30
7.35
8.40
9.45
10.50
11.55

did u get the trick ?
after jotting down 1.05, 2.10 etc. u just have to add 05 in the min. place, its like the table of 5.

Answer 7

1:05

Answer 8

a little bit AFTER 1:05 pm

Answer 9

1:05
2:10
3:15
4:20
etc
etc
etc