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Math Help - Angles of a clock

  1. #1
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    Lightbulb Angles of a clock

    A clock gains five minutes every hour, the angle traversed by the second hand in one minute will be which one of the following:
    a.
    360
    b. 360.5

    c. 390
    d. 375


    I want a detailed solution. Merely the answer won't do.

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  2. #2
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    Quote Originally Posted by radha's consciousness View Post
    A clock gains five minutes every hour, the angle traversed by the second hand in one minute will be which one of the following:
    a.
    360
    b. 360.5

    c. 390
    d. 375


    I want a detailed solution. Merely the answer won't do.

    To rephrase, the statement of the problem says
    "A clock gains 300 seconds every 3600 seconds; find the angle that the second hand traverses in one minute."

    So the clock says 3900 seconds have passed every 3600 seconds.
    Then, 65 seconds pass on the clock every 60 seconds.
    Then, 65 seconds pass on the clock every minute.

    The question is now, how many degrees will the second hand traverse after 65 seconds pass on the clock? Every 5 seconds on the clock, we see that the second hand traverses 30. So in 65 seconds on the clock, it has traversed 390. The answer is 390.

    Did my solution make sense?
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  3. #3
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    Lexington, MA (USA)
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    Hello, radha's consciousness!

    My solution is similar to math84's.


    A clock gains five minutes every hour.
    The angle traversed by the second hand in one minute will be:

    . . a. 360 . . b. 360.5 . . c. 390 . . d. 375
    This clock moves 65 minutes every 60 minutes.

    . . Each hand moves \frac{65}{60} = \frac{13}{12} as far as it should.


    A correct second hand moves 360 in one minute.

    . . This second hand moves: . \frac{13}{12}\times 360^o \:=\:{\color{blue}390^o} in one minute.


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