Results 1 to 7 of 7

Math Help - A new "Work" problem

  1. #1
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,739
    Thanks
    645

    A new "Work" problem

    A and B can paint a room in \frac{12}{7} hours.
    B and C can paint the room in 6 hours.
    A and C can paint the room in 12 hours.

    How long would each take to paint the room if working alone?

    [Any comments on C ?]

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Soroban View Post
    A and B can paint a room in \frac{12}{7} hours.
    B and C can paint the room in 6 hours.
    A and C can paint the room in 12 hours.

    How long would each take to paint the room if working alone?

    [Any comments on C ?]

    You can use my trick.
    If one does work in x the other in y. Then together it takes.
    \frac{xy}{x+y}
    Thus,
    \frac{AB}{A+B}=\frac{12}{7}
    \frac{BC}{C+B}=6
    \frac{AC}{A+C}=12
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,739
    Thanks
    645

    Anyone? Anyone?

    So far, 25 views and only TPHacker has responded.

    Hasn't anyone solved it? .The humor is in the solution.
    . . (Am I the only one laughing?)

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,939
    Thanks
    338
    Awards
    1
    Quote Originally Posted by Soroban View Post
    So far, 25 views and only TPHacker has responded.

    Hasn't anyone solved it? .The humor is in the solution.
    . . (Am I the only one laughing?)

    I think that B is the most interesting. Gets the room painted 2 hours before he even walks in. (C must be using paint remover....)

    -Dan
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,739
    Thanks
    645

    Solution


    Suppose A can paint the room in a hours,
    . . . . . . B can paint the room in b hours,
    . . . . . . C can paint the room in c hours.

    In one hour, A can paint \frac{1}{a} of the room.
    In one hour, B can paint \frac{1}{b} of the room.
    In one hour, C can paint \frac{1}{c} of the room.

    In one hour, A and B can paint \frac{1}{a} + \frac{1}{b} of the room.
    Since it takes both of them \frac{12}{7} hours together,
    . . in one hour, they can paint \frac{7}{12} of the room: . \frac{1}{a} + \frac{1}{b}\:=\:\frac{7}{12} . [1]

    In one hour, B and C can paint \frac{1}{b} + \frac{1}{c} of the room.
    Since it takes both of them 6 hours together,
    . . in one hour, they can paint \frac{1}{6} of the room: . \frac{1}{b} + \frac{1}{c} \:=\:\frac{1}{6} . [2]

    In one hour, A and C can paint \frac{1}{a} + \frac{1}{c} of the room.
    Since it take both of them 12 hours,
    . . in one hour, they can paint \frac{1}{12} of the room: . \frac{1}{a} + \frac{1}{c} \:=\:\frac{1}{12} . [3]


    Subtract [2] from [1]: . \frac{1}{a} - \frac{1}{c} \:=\:\frac{5}{12}
    . . . . . . . . . .Add [3]: . \frac{1}{a} + \frac{1}{c}\:=\:\frac{1}{12}

    And we have: . \frac{2}{a} \,= \,\frac{1}{2}\quad\Rightarrow\quad \boxed{a\,=\,4}

    Substitute into [1]: . \frac{1}{4} + \frac{1}{b} \:=\:\frac{7}{12}\quad\Rightarrow\quad \boxed{b\,=\,3}

    Substitute into [3]: . \frac{1}{4} + \frac{1}{c}\:=\:\frac{1}{12}\quad\Rightarrow\quad \boxed{c\,=\,-6}


    Punchline: C does negative work.

    As Dan pointed out, C must be using paint remover.

    (Their names must be: Curly, Larry and Moe.)

    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    C would be a very annoying partner
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2005
    Posts
    21
    I guess that makes since; A and B by themselves have the room done in less than two hours but C makes them take many hours longer.

    I'm probably person C XP.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 6th 2011, 03:00 PM
  2. Replies: 2
    Last Post: July 22nd 2010, 10:15 AM
  3. Replies: 2
    Last Post: July 21st 2010, 05:54 PM
  4. Replies: 2
    Last Post: December 26th 2008, 04:57 PM
  5. A "work" word problem, need help!
    Posted in the Algebra Forum
    Replies: 1
    Last Post: June 20th 2008, 01:25 AM

Search Tags


/mathhelpforum @mathhelpforum