Clock

How many times a day hands on a clock overlap?

Correct result:

n =  22

Solution:

α=β \alpha = \beta

36060m+360k=36012m60\dfrac{ 360 ^\circ }{ 60} m + 360 ^\circ k = \dfrac{ 360 ^\circ }{ 12}\dfrac{ m}{ 60}

6m+360k=0.5m6 ^\circ m + 360 ^\circ k = 0.5 ^\circ m

6m -0 = m/2; m = 2/11*0 = 0 min ==> 0:00:00
6m -360 = m/2; m = 2/11*360 = 65.45 min ==> 1:05:27
6m -720 = m/2; m = 2/11*720 = 130.91 min ==> 2:10:54
6m -1080 = m/2; m = 2/11*1080 = 196.36 min ==> 3:16:21
6m -1440 = m/2; m = 2/11*1440 = 261.82 min ==> 4:21:49
6m -1800 = m/2; m = 2/11*1800 = 327.27 min ==> 5:27:16
6m -2160 = m/2; m = 2/11*2160 = 392.73 min ==> 6:32:43
6m -2520 = m/2; m = 2/11*2520 = 458.18 min ==> 7:38:10
6m -2880 = m/2; m = 2/11*2880 = 523.64 min ==> 8:43:38
6m -3240 = m/2; m = 2/11*3240 = 589.09 min ==> 9:49:05
6m -3600 = m/2; m = 2/11*3600 = 654.55 min ==> 10:54:32
6m -3960 = m/2; m = 2/11*3960 = 720 min ==> 12:00:00
6m -4320 = m/2; m = 2/11*4320 = 785.45 min ==> 13:05:27
6m -4680 = m/2; m = 2/11*4680 = 850.91 min ==> 14:10:54
6m -5040 = m/2; m = 2/11*5040 = 916.36 min ==> 15:16:21
6m -5400 = m/2; m = 2/11*5400 = 981.82 min ==> 16:21:49
6m -5760 = m/2; m = 2/11*5760 = 1047.27 min ==> 17:27:16
6m -6120 = m/2; m = 2/11*6120 = 1112.73 min ==> 18:32:43
6m -6480 = m/2; m = 2/11*6480 = 1178.18 min ==> 19:38:10
6m -6840 = m/2; m = 2/11*6840 = 1243.64 min ==> 20:43:38
6m -7200 = m/2; m = 2/11*7200 = 1309.09 min ==> 21:49:05
6m -7560 = m/2; m = 2/11*7560 = 1374.55 min ==> 22:54:32
6m -7920 = m/2; m = 2/11*7920 = 1440 min ==> 24:00:00 !!! h>23

6m -8280 = m/2; m = 2/11*8280 = 1505.45 min ==> 25:05:27 !!! h>23



n=22




Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 1 comment:
#
Bo Shag
I dislike these questions, but they are very good for the brain.

avatar









Tips to related online calculators
Do you solve Diofant problems and looking for a calculator of Diofant integer equations?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Do you want to convert length units?
Do you want to convert velocity (speed) units?
Do you want to convert time units like minutes to seconds?
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • What time is it?
    clocks2_1 What time is it, when there is 4 times less time left until midnight than the time that has elapsed since noon? What time is it, when one-fifth of the hours that have passed since midnight is equal to one-third of the hours that are missing by 12 o'clock?
  • Book reading
    kniha_tridni Suzan reads a book. If she read half an hour a day, she would read it in nine days. How many minutes does he have to read a day if he wants to read it three days earlier?
  • The tourist
    tourist The tourist walked a quarter of the way on the first day, a third of the rest on the second day, and 20 km on the last day. How many km did he walk in three days?
  • Work together
    time Two bricklayers plastering a wall. The first would plaster it in 8 hours, the second in 12 hours. How many hours will they be done with the work if they work together?
  • Five combers
    permutations_3 Five combers harvest 12 rows of strawberries in 4 hours. How many rows of strawberries will two combers harvest in 10 hours?
  • Cable car
    lanovka The cable car will carry 1280 passengers in 40 minutes. How many people will be transported in 2.5 hours?
  • What is
    exp_growth2 What is the annual percentage increase in the city when the population has tripled in 20 years?
  • The field
    tractors 3 tractors plow the field in 6 hours. However, after 2 hours, 1 tractor broke down. How long will the field be plowed?
  • Five tractors
    tractors Five tractors plow the fields in 4.8 hours. How long will it take to plow the field when, after an hour and a half of work, two tractor drivers have been called up for another task?
  • The half life
    exp_growth2 The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 145 grams of a radioactive isotope, how much will be left after 3 half-lives?
  • Slow saving in banks
    penize_5 How long will it take to save € 9,000 by depositing € 200 at the beginning of each year at 2% interest?
  • Fighter
    vyskovy uhol A military fighter flies at an altitude of 10 km. From the ground position, it was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h.
  • Birthday paradox
    holland How large must the group of people be so that the probability that two people have a birthday on the same day of the year is greater than 90%?
  • Age of family
    age The age of father and son is in the ratio 10: 3. The age of the father and daughter is in ratio 5: 2. How old are a father and a son if the daughter is 20?
  • Motorcycle engine
    motor_rpm The motorcycle engine has a constant power of 1.2 kW for 0.5 hours. How much work does the engine do? Express work in kWh and Ws units.
  • Electric work
    bulb Calculate the work done by the electric forces passing the current of 0.2 A through the bulb in 10 minutes if the bulb is connected to a 230 V power supply.
  • Cyclist 12
    cyclist What is the average speed of a cycle traveling at 20 km in 60 minutes in km/h?