At what timing are both hands of a clock going to be exactly on top of each other?

Question

We all know when its 12 o clock the small hand and the big hand on the clock are exactly one over each other.
But then the exact same thing happens at 1:05 and a few secs, then 2:10 and a few secs.
Any of you know the exact time and seconds when the big hand and the small hand will be on over another.

Hope you guys can help

Answer 1

The times mentioned are not the exact answers.



Let x be the number of minutes so that the hour hand and the minute hand overlaps after a time of A o'clock.



Thus A = 0,1,2,3, ... ,10



Then at A o'clock, the hour hand is at the number A.

Also, if the minute hand is 12 times faster than the hour hand. Thus if the minute hand had traveled for x, then the hour hand had traveled for x/12



The equation is now:

5A + x/12 = x

5A = 11x/12

x = 60A/11 ... this is the number of minutes when they would overlap



thus at 1:00 (A = 1)

x = 60/11 ≈ 5.454545 minutes



thus the exact times are:

1 : 05 & 5/11 min = 1 : 05 min 27 3/11 seconds

2 : 10 & 10/11 min = 2 : 10 min 54 6/11 seconds

3 : 16 & 4/11 min

4 : 21 & 9/11 min

5 : 27 & 3/11 min

6 : 32 & 8/11 min

7 : 38 & 2/11 min

8 : 43 & 7/11 min

9 : 49 & 1/11 min

10:54 & 6/11 min

the next time they would overlap is again at 12:00 .



just convert the rest of the fractional part of the minutes to seconds (multiply by 60 .)

Answer 2

Minute hand rotates 360° in 1 hr i.e. 360/60= 6° in 1 min.

hour hand rotates 360° in 12 hr i.e. 360/720= 1/2° in 1 min.

difference in two hands = 6 – 1/2 = 11/5 degree.

two hands overlap means they rotate through 360°

for 11/2 degree requirs 1 min

so 360° requires 360 × 2/11 = 65 5/11 min. = 1 hr 5 min 27.27 sec.

1) 12 :00

2) 12 + 1 hr 5 min 27.27 sec.13 hr 5 min 27.27 sec.

3) 13 hr 5 min 27.27 sec. + 1 hr 5 min 27.27 sec.14 hr 10 min 54.54 sec.

and so on.

or you can calculate the hours lap after 12

if it is 5 hr then in 5 hr. 5 × 65 5/11 = 327 3/11 min lap

time = 12:00 + 327 3/11 min = 12 + 5 hr 27 min 27.27 sec.

----------

Answer 3

12:00, 1:05, 2:10, 3:15, 4:20, 5:25, 6:30, 7:35, 8:40, 9:45, 10:50 & 11:55.....

This will happen twice a day... So U have it 24 times a day!!!



Is this wat U were asking for???

Answer 4

a close-by sheriff became into finding for a deputy, so a blonde went in to test for the interest. "ok," the sheriff drawled, "what's one and one?" "11," she spoke back. The sheriff concept to himself, "it is not what I meant, yet she's precise." Then the sheriff asked, "What 2 days of the week initiate with the letter T?" "immediately and the following day," spoke back the blonde. He became into lower back shocked that the blonde presented a splendid answer that he had in no way considered himself. "Now, hear intently, who killed Abraham Lincoln?" asked the sheriff. The blonde appeared slightly shocked herself, then concept fairly troublesome for a minute and finally admitted, "i do no longer understand." The sheriff spoke back, "properly, why do no longer you pass abode and artwork on that one for a on a similar time as?" So, the blonde wandered over to the ask your self parlor, the place her friends have been waiting to hearken to the end results of the interview. The blonde became into exultant. "It went great! First day on the interest and that i'm already engaged on a homicide case!"

Answer 5

Just like Sweety Pie said, it happens a lot. 24 times. Though I'm not gonna go and list all the times when she's done it for me.

Answer 6

3.30 and 30 seconds