Results 1 to 3 of 3

Math Help - Trigonometry

  1. #1
    Super Member
    Joined
    Jun 2008
    Posts
    829

    Trigonometry

    A man begin the trip when the hands of the clock are attached between 8 and 9 hours; the journey ends when the child pointer is between 14 and 15 hours and the pointer larger is 180 the other. How long the trip lasted ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    644
    Hello, Apprentice123!

    I believe I've translated your problem to English . . .


    A man begin the trip when the hands of the clock are together between 8:00 and 9:00.
    The journey ends when the hour hand is between 14:00 and 15:00 hours
    and the minute hand is diametrically opposite. .How long did the trip last?
    The minute hand moves at 6 degress/minute.
    . . In t minutes, M moves: 6t degrees.

    The hour hand moves at degrees/minute.
    . . In t minutes, H moves: \tfrac{1}{2}t degrees.


    At 8:00, the minute hand is at 0; the hour hand is at 240.
    . . In t minutes, M is at 6t degrees . . . and H is at 240 + \tfrac{1}{2}t degrees.
    The hands are together: . 6t \:=\:\tfrac{1}{2}t + 240 \quad\Rightarrow\quad t \:=\:\frac{480}{11} \:=\:43\tfrac{7}{11}
    . . The trip started at: . 8\!:\!43\tfrac{7}{11} a.m.


    At 2:00, M is at 0; H is at 60.
    In t minutes, M is at 6t degrees . . . and H is at 60 + \tfrac{1}{2}t degrees.
    The hands are 180 apart: . 6t \:=\:(60+\tfrac{1}{2}t) + 180 \quad\Rightarrow\quad t \:=\:\frac{480}{11} \:=\:43\tfrac{7}{11}
    . . The trip ended at: . 2\!:\!43\tfrac{7}{11} p.m.


    Therefore, the trip took exactly 6 hours.

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2008
    Posts
    829
    Thank you, sorry my english
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometry to Memorize, and Trigonometry to Derive
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: August 21st 2013, 12:03 PM
  2. How To Do Trigonometry For This...?
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: January 10th 2009, 05:56 PM
  3. How To Do This Trigonometry
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 3rd 2009, 01:55 AM
  4. trigonometry
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 31st 2008, 08:06 PM
  5. Trigonometry
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 18th 2008, 04:40 PM

Search Tags


/mathhelpforum @mathhelpforum