Results 1 to 3 of 3

Math Help - Right angles and clock

  1. #1
    Newbie
    Joined
    Feb 2008
    From
    Auckland, NZ
    Posts
    16

    Lightbulb Right angles and clock

    Hamilton High School starts at 8.30am and finishes at 3.30pm each day. The number of time the hour and minute hand form a right angle on the school clock during the day is?

    Is it 13 or 14 but why is it so?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,686
    Thanks
    617
    Hello, clarebear14!

    Hamilton High School starts at 8:30 am and finishes at 3:30 pm each day.
    The number of times the hour and minute hand form a right angle
    on the school clock during the day is ...?
    There is no formula for this problem.
    . . We must make a series of sketches.

    I found twelve times.

    The times (approximate) are: .9:00, 9:30, 10:05, 10:35, 11:10, 11:45,
    . . 12:15, 12:50, 1:20, 1:55, 2:25, 3:00


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    Note: Three-thirty is not included.

    At 3:30, the hour hand is halfway between 3 and 4,
    . . forming a 105 angle with "12".
    So the minute hand would form a 195 angle with "12",
    . . indicating a time after three-thirty.

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by clarebear14 View Post
    Hamilton High School starts at 8.30am and finishes at 3.30pm each day. The number of time the hour and minute hand form a right angle on the school clock during the day is?

    Is it 13 or 14 but why is it so?
    The time period between 2 right angles is \frac6{11} \ hours. (Half an hour plus the half of \frac1{11} hour)

    Divide the time span from 08:30 am to 03:30 pm = 7 hours by \frac6{11} you'll get \left(12 + \frac56\right)\ times

    So it happens 12 times that the hands of the clock form a right angle.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. clock puzzle
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: May 3rd 2011, 11:08 PM
  2. angles between clock hands of the Time = 11:08
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: November 29th 2010, 12:25 PM
  3. Angles of a clock
    Posted in the Geometry Forum
    Replies: 2
    Last Post: August 26th 2009, 08:46 AM
  4. Replies: 1
    Last Post: January 7th 2009, 06:07 PM
  5. The Clock
    Posted in the Math Topics Forum
    Replies: 6
    Last Post: January 11th 2007, 02:27 AM

Search Tags


/mathhelpforum @mathhelpforum