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Watch problems gaining and losing time

  1. Dec 3, 2015 #1
    1. My watch (which is a 12 hour watch) gains 3 minutes every 2 hours.

    a) I set my watch to the correct time at noon on 1st January. If I don't reset it, when will it next show the correct time?

    I got 48 hours after, so that's at noon on the 3rd January. as if my watch gains 3 minutes every two hours then over 24 lots of 2 hours, it would have gained an extra 2 hours. So that is 24 lots of 2 hours = 24 x 2 = 48 hours added to the 'correct' starting time of noon. Hence, my answer of noon on the 3rd January.


    2. Mrs Varma's watch (also a 12 hour watch) loses 5 minutes every 2 hours. She also sets her watch to the correct time at noon on 1st January.

    b) When will our two watches next show the same time?

    I am completely stuck here :(... please help to explain to me how to do this...



    3. When will our watches next show the same, CORRECT time?

    Again, I can't do this... Any explanation would be greatly appreciated. Thank you.

    Nat.
     
  2. jcsd
  3. Dec 3, 2015 #2

    Samy_A

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    If you watch gains 3 minutes in 2 hours, it gains 3*12=36 minutes in a day. So it can't show the correct time after only two days.
    Try to write the time on your watch as a function of the correct time.
    Say ##W(t)=## some function of the correct time ##t## (expressed in minutes)
    Then for your clock to again show the correct time, you should have ##W(t)=t+720## (because there are 720 minutes in 12 hours, and your clock has to gain 12 hours to again show the correct time). Solve that equation for ##t##.

    Use another similar function to represent the time on Mrs Varma's watch to solve 2) and 3).
     
    Last edited: Dec 3, 2015
  4. Dec 3, 2015 #3
    Ok, I got January 4th at 8pm. Is this correct?

    Cannot do 2b nor 3. Can anyone help me?
     
  5. Dec 3, 2015 #4

    Samy_A

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    It would help if you showed how you got that result.
    I find something different. Note that your watch only gains 36 minutes a day, so it can't catch up in 3 days and 8 hours.

    The time on your watch can be expressed as ##W(t)=t+t*3/120##, where ##t## is the correct time in minutes, and ##t=0## represents noon on 1st January.
    Your watch will again show the correct time when ##W(t)=t+720##.

    So we look for the solution of $$t+t*3/120=t+720$$
    Express the time on Mrs Varma's watch by a function ##V(t)##, similar to the function ##W(t)## expressing the time on your watch.
     
    Last edited: Dec 3, 2015
  6. Dec 3, 2015 #5

    PeroK

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    Why not try this to get you started and let you see what's going on. Keep two lists: one with the correct time and one with the time your watch shows. For 1a:

    Correct Time / My Watch

    Jan 1st noon / noon
    Jan 1st 2.00 (pm) / 2.03
    Jan 1st 4.00 (pm) / 4.06
    Jan 1st 6.00 (pm) / 6.09

    You might first ask yourself: when is your watch an hour ahead?
     
  7. Dec 3, 2015 #6
    Ok,

    a) I set my watch to the correct time at noon on 1st January. If I don't reset it, when will it next show the correct time?

    I got 8pm (or 20.00) on 4th January. Can someone tell me if I am right?


    2. Mrs Varma's watch (also a 12 hour watch) loses 5 minutes every 2 hours. She also sets her watch to the correct time at noon on 1st January.

    b) When will our two watches next show the same time?

    I got 25th January at noon (lunchtime). Am I right?


    3. When will our watches next show the same, CORRECT time?

    I got 19th February at noon (lunchtime). Am I right?
     
  8. Dec 3, 2015 #7

    Samy_A

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    No, not correct.
    No, not correct.

    No, not correct.


    If you find my approach with the function too difficult, why don't you try what @PeroK suggested for 1a)?
     
  9. Dec 3, 2015 #8

    PeroK

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    Given your answer to 1a, I don't think you've understood the problem. Imagine your watch really was 3 mins fast every 2 hours, that's only 36 minutes a day. It will, therefore, take weeks until it shows the correct time again.

    I wouldn't look at questions 2 and 3 until you've understood problem 1. Go back to my suggestion in post #5 to give yourself an idea of what's happening.
     
  10. Dec 3, 2015 #9
    if it gains 36mins in every 24 hours then for my watch to catch up time it will have to be 1440/36 = 40 so forty days from 1st of January which would be 10th February at noon.

    Is this correct?
     
  11. Dec 3, 2015 #10

    haruspex

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    Much better, but remember it is a 12 hour watch. How fast will it be when it first shows the correct time?
     
  12. Dec 3, 2015 #11

    PeroK

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    That's much closer.

    How many hours (on a 12-hour watch) does it need to gain to catch up? The question assumes you know that on a 12-hour watch, no distinction is made between 12 noon and 12 midnight. Perhaps you're one of those people who never wears a watch?
     
  13. Dec 3, 2015 #12
    Oh!! I did not know about this! It's so confusing... No I do not have a watch, and only really get 24hrs clocks.

    is it 20 days later? Is it 720/36 = 20 so on 21st of January at noon. If so, why?
     
  14. Dec 3, 2015 #13

    PeroK

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    I think you've got the idea. Here's the sort of thing they're talking about:

    clock-face-illustration-dial-as-part-analog-watch-black-red-pointers-31930665.jpg
     
  15. Dec 3, 2015 #14

    Samy_A

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    Yes.

    Your watch has to gain 12 hours, that's 12*60=720 minutes. As it gains 36 minutes a day, it shows the correct time again after 720/36=20 days.
     
  16. Dec 3, 2015 #15
    I see! Thanks.... So for:

    2)
    Thanks :)... Much clearer!
     
  17. Dec 3, 2015 #16
    Not sure how to go about 2 and 3
     
  18. Dec 3, 2015 #17

    haruspex

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    How far apart are the two watches after one hour? How far apart do they need to be to be showing the same time?
     
  19. Dec 3, 2015 #18
    they are 8 mins apart... then 16 then 24.. Ahhh so when does 8 fit into multiples of 60, right?
     
  20. Dec 3, 2015 #19
    8
    16
    24
    32
    40
    48
    56
    64
    72
    80
    88
    96
    104
    112
    120

    So that's 30 hours after.... So that would be 2nd January at 6pm? Is this right?
     
  21. Dec 3, 2015 #20

    haruspex

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    I said "after one hour".
    And you did not answer my second question: how far apart will they be when they first show the same time again?
     
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