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Math Help - Problem Solving

  1. #1
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    Problem Solving

    Harry, Annie and Mitch decided to paint the living room. Harry could paint the room by himself in 3 hours. Annie could do it in 4 hours and Mitch would take 6 hours on his own. If they all work together and dont get in each others way, how long will the job take?
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by not happy jan View Post
    Harry, Annie and Mitch decided to paint the living room. Harry could paint the room by himself in 3 hours. Annie could do it in 4 hours and Mitch would take 6 hours on his own. If they all work together and dont get in each others way, how long will the job take?

    Since Harry can paint the room in 3 hours he can paint the \frac{1}{3} of the room in 1 hour.

    Using the same argument for the other's we get

    Annie \frac{1}{4} of the room in 1 hour

    Mitch \frac{1}{6} of the room in 1 hour

    Now we can add the rates that each of them work

    \underbrace{\left(\frac{1}{3}+\frac{1}{4} +\frac{1}{6}\right)}_{\mbox{how fast they are together}}\cdot \underbrace{t}_{time}=\underbrace{1}_{\mbox{one room}}

    Simplifying we get

    \frac{3}{4}t=1 \iff t=\frac{4}{3} so it will take them One and one thirds hours or 1 hour and 20 min.

    I hope this helps.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Why are you not happy, Jan?
    Quote Originally Posted by not happy jan View Post
    Harry, Annie and Mitch decided to paint the living room. Harry could paint the room by himself in 3 hours. Annie could do it in 4 hours and Mitch would take 6 hours on his own. If they all work together and dont get in each others way, how long will the job take?
    just add their rates. let painting the living room be the job

    for Harry, he does \frac {1 \mbox{ Job}}{3 \mbox{ Hours}}

    Annie does \frac {1 \mbox{ Job}}{4 \mbox{ Hours}}

    Mitch does \frac {1 \mbox{ Job}}{6 \mbox{ Hours}}

    together they can do: \frac 13 + \frac 14 + \frac 16 = \frac 34 = \frac 1{4/3} that is, \frac {1 \mbox{ Job}}{{\color{red}4/3 \mbox{ Hours}}}

    EDiT: Thanks a lot, TES you look different with long hair
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