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  1. #1
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    Question word problems

    how to do this? i'm confused..

    If A, B, and C work together in a job, it will take 1 1/3 hours. If only A and B work, it will take 1 5/7 hours. But if B and C work, it would take 2 2/5 hours. How long would it take each man working alone, to complete the job?

    Thanks..
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  2. #2
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    Quote Originally Posted by princess_21 View Post
    how to do this? i'm confused..

    If A, B, and C work together in a job, it will take 1 1/3 hours. If only A and B work, it will take 1 5/7 hours. But if B and C work, it would take 2 2/5 hours. How long would it take each man working alone, to complete the job?

    Thanks..
    Time to complete the job by A: x hours
    Time to complete the job by B: y hours
    Time to complete the job by C: z hours

    When all works together T(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})=1, where T=1 1/3 hours

    When A and B works: T'(\frac{1}{x}+\frac{1}{y})=1, where T'=1 5/7 hours

    When B and C works: T''(\frac{1}{y}+\frac{1}{z})=1, where T'' = 2 2/5 hours

    Solve for x,y&z
    Hope this helps
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  3. #3
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    Quote Originally Posted by princess_21 View Post
    If A, B, and C work together in a job, it will take 1 1/3 hours. If only A and B work, it will take 1 5/7 hours. But if B and C work, it would take 2 2/5 hours. How long would it take each man working alone, to complete the job?
    For "work" word problems, it's often best to start by converting the times to rates. For instance, if you can complete some task in three hours (the time), then you can do 1/3 of it each hour (the rate). If I take four hours to do the same thing, then I do only 1/4 of it each hour. If we worked together, we'd do 1/3 + 1/4 = 7/12 of it each hour.

    In your case:

    . . . . .A's rate: 1/a
    . . . . .B's rate: 1/b
    . . . . .C's rate: 1/c

    You are given that the time for A & B together is 12/7 hours, the time for B & C together is 12/5 hours, and the time for all three together is 4/3 hours. Then:

    . . . . .A & B together: 1/a + 1/b = 7/12
    . . . . .B & C together: 1/b + 1/c = 5/12
    . . . . .all three together: 1/a + 1/b + 1/c = 3/4

    This gives you three rational equations in three unknowns (ouch!). I'd start by subtracting the first line above from the third, giving us:

    . . . . . \frac{1}{c}\, =\, \frac{2}{12}\, =\, \frac{1}{6}

    Solve this for the value of "c". Then subtract the second line from the third line, and solve the result for the value of "a". Plug this value into the first equation, and back-solve for the value of "b".

    If you get stuck, please reply showing your steps and reasoning so far. Thank you!
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  4. #4
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    Quote Originally Posted by stapel View Post
    For "work" word problems, it's often best to start by converting the times to rates. For instance, if you can complete some task in three hours (the time), then you can do 1/3 of it each hour (the rate). If I take four hours to do the same thing, then I do only 1/4 of it each hour. If we worked together, we'd do 1/3 + 1/4 = 7/12 of it each hour.

    In your case:

    . . . . .A's rate: 1/a
    . . . . .B's rate: 1/b
    . . . . .C's rate: 1/c

    You are given that the time for A & B together is 12/7 hours, the time for B & C together is 12/5 hours, and the time for all three together is 4/3 hours. Then:

    . . . . .A & B together: 1/a + 1/b = 7/12
    . . . . .B & C together: 1/b + 1/c = 5/12
    . . . . .all three together: 1/a + 1/b + 1/c = 3/4

    This gives you three rational equations in three unknowns (ouch!). I'd start by subtracting the first line above from the third, giving us:

    . . . . . \frac{1}{c}\, =\, \frac{2}{12}\, =\, \frac{1}{6}

    Solve this for the value of "c". Then subtract the second line from the third line, and solve the result for the value of "a". Plug this value into the first equation, and back-solve for the value of "b".

    If you get stuck, please reply showing your steps and reasoning so far. Thank you!
    . \frac{1}{c}\, =\, \frac{2}{12}\, =\, \frac{1}{6}

    i think i'm getting to the answer.
    i will post my answers later, please try to check.
    thank you very much
    Last edited by princess_21; March 30th 2009 at 06:06 AM. Reason: error
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  5. #5
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    1/A + 1/B + 1/C= 3/4
    1/A + 1/B= 7/12
    1/B + 1/C= 5/12


    1/A=1/3
    1/B=1/4
    1/C=1/6

    then
    A= 3 hrs.
    B=4 hrs.
    C=6 hrs.
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