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KevinFinity12-Amethyst
12-Amethyst
February 17, 2022
Solved

A simple challenge

  • February 17, 2022
  • 6 replies
  • 8272 views

Here is a simple math challenge for you. Solve with MathCAD!

 

On a regular 12 hour clock, how often does the minute hand pass the hour hand?

(Hint: The answer is not 60 minutes.)

Edit: I'm looking for the amount of time it takes for the minute hand to pass the hour hand.

 

I will post the solution in 1 week. Kudos abound!

Best answer by Werner_E
Edit: I'm looking for the amount of time it takes for the minute hand to pass the hour hand.

 

That depends on how thick the hands are 🙂

 

I guess that you mean the time between one pass of hands and the next one, right? I already wrote in an answer above that its exactly 12/11 of an hour. At least if we assume that the hands move continually and not stepwise 😉

@unknown also mentioned that it happens 11 times in a period of 12 hours which also makes for an interval of 12/11 hours.

6 replies

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Werner_E25-Diamond I
25-Diamond I
February 17, 2022
@KevinFinity wrote:

Here is a simple math challenge for you. Solve with MathCAD!

 

On a regular 12 hour clock, how often does the minute hand pass the hour hand?

(Hint: The answer is not 60 minutes.)

 

Since you are asking for a number, the solution cannot have the dimension "time" anyway 🙂

 

Also you sure mean "during a time period of 12 hours".

 

Anyway - challenge accepted. Lets use Mathcad 15 to simply watch and count (and stop before we reach 12:00):

Clock.gif

 

    W
    Werner_E25-Diamond I
    25-Diamond I
    February 18, 2022

    A similar question comes to my mind now:

    If you exchange minute and hour handle so the the smaller hour handle now makes a full turn in 60 minutes, most of the time the handles will be in a position which does not show a valid time. How many times in a period of 12 hours the handles will show a correct, possible time?

      F
      Fred_Kohlhepp23-Emerald I
      23-Emerald I
      February 19, 2022

      Very interesting!

      The answer to Werner's question is "as the hands of the two clocks mark the hour positions, starting from 12 o'clock thru 11 o'clock, eleven times in twelve hours."

       

       

        A
        Anonymous
        February 18, 2022
        @KevinFinity wrote:

        Here is a simple math challenge for you. Solve with MathCAD!

         

        On a regular 12 hour clock, how often does the minute hand pass the hour hand?

        (Hint: The answer is not 60 minutes.)

         

        I will post the solution in 1 week. Kudos abound!

        The easiest answer I can give is based on the first twelve hours of a clock face (I'll double it at the end).

        For each revolution of the minute hand, the hour hand moves one twelfth of the trip around the face, or 30 degrees. This however is assuming the same starting point on the minutes for each revolution but this is not so. Ultimately one revolution of the twelve hours must be subtracted due to the hour's constant transit around the face. This gives us eleven (11) times in 12 hours where the hands will coincide.

        Double the eleven to get the value for a 24 hour period which is 22.

        (12–1)*2=22

          K
          KevinFinity12-AmethystAuthor
          12-Amethyst
          February 18, 2022

          You're correct, but that's not the answer I'm looking for. I apologize for how I worded the question originally. I'm looking for the precise amount of time it takes for the minute hand to pass the hour hand.

          L
          LucMeekes23-Emerald IV
          23-Emerald IV
          February 18, 2022

          On 'regular clocks' both hands move stepwise. This is most obviously shown by the 'seconds' hand, but also the minutes and the hours hands move stepwise, though it may be with very small steps.

          Now the speed with which each hand turns to the next step is unspecified. How 'precise' do you think you can get the time?

           

          Luc

            F
            Fred_Kohlhepp23-Emerald I
            23-Emerald I
            February 18, 2022

            Simple problem;  simple answer:

            Fred_Kohlhepp_0-1645187817535.png

            (This could be animated in 15!

             

              W
              Werner_E25-Diamond I
              25-Diamond I
              February 18, 2022

              @Fred_Kohlhepp 

              @Fred_Kohlhepp wrote:

              Simple problem;  simple answer:

              Maybe not that simple 😉

              Your reply is missing the actual answer to "how often".

              Furthermore only every second point of intersection is a valid solution!

              Werner_E_0-1645192328662.png

              12 of those 23 solutions are not valid!

               

              E.g. the "solution" t = 12/13 hr = 55.385 min corresponds to 00:55:23.077.

              At this time the handles do not pass but are mirrored by the vertical

              Werner_E_1-1645191798425.png

              The times we are looking for simply are all multiples of 12/11 hours.

               

                F
                Fred_Kohlhepp23-Emerald I
                23-Emerald I
                February 18, 2022

                Your reply is missing the actual answer to "how often".

                The times we are looking for simply are all multiples of 12/11 hours.

                Fred_Kohlhepp_0-1645213149573.png

                really?

                But you get credit for a really nice animation!  

                 

                  W
                  Werner_E25-Diamond IAnswer
                  25-Diamond I
                  February 18, 2022
                  Edit: I'm looking for the amount of time it takes for the minute hand to pass the hour hand.

                   

                  That depends on how thick the hands are 🙂

                   

                  I guess that you mean the time between one pass of hands and the next one, right? I already wrote in an answer above that its exactly 12/11 of an hour. At least if we assume that the hands move continually and not stepwise 😉

                  @unknown also mentioned that it happens 11 times in a period of 12 hours which also makes for an interval of 12/11 hours.

                    D
                    DJF16-Pearl
                    16-Pearl
                    February 18, 2022

                    I thought it'd be fun to think of it as distance travelled instead of angle.  Similar to Fred's otherwise.

                    2022-02-18_13-01-28.png

                      K
                      KevinFinity12-AmethystAuthor
                      12-Amethyst
                      March 1, 2022

                      Hello, everyone. Here is my solution. I modeled it as an infinite series and came up with the same results. It was very interesting to see the variety of different ways to get the same answer. Everybody thinks a bit differently, and that's what I wanted to see. Thank you all for participating.

                       

                      KevinFinity_0-1646164399137.png

                       

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