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Math Help - Need help with a rate/time problem

  1. #1
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    Need help with a rate/time problem

    Abbie paints twice as fast as Beth and three times as fast as Cathie. If it takes them 60 min to paint a living room with all 3 working together, how long would it take Abbie if she works alone?

    So far this is what I got:

    Rate Distance Time
    Cathies 3x 1 1/3x
    Beth 2x 1 1/2x
    Abbie x 1 1/x

    I then did (1/2x)+(1/3x)+(1/x)=1

    Can someone explain to me where I keep going wrong? Thanks
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  2. #2
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    Quote Originally Posted by coolieman View Post
    Abbie paints twice as fast as Beth and three times as fast as Cathie. If it takes them 60 min to paint a living room with all 3 working together, how long would it take Abbie if she works alone?

    So far this is what I got:

    Rate Distance Time
    Cathies 3x 1 1/3x
    Beth 2x 1 1/2x
    Abbie x 1 1/x

    I then did (1/2x)+(1/3x)+(1/x)=1

    Can someone explain to me where I keep going wrong? Thanks
    here only abbie can do painting in 50 nminutes.
    that is let abbie=x
    beth=2x
    cathies=3x
    so x+2x+3x=6x
    6x can paint in 60min
    x=10minutes
    60-10=50minutes.
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  3. #3
    MHF Contributor
    Joined
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    Quote Originally Posted by coolieman View Post
    Abbie paints twice as fast as Beth and three times as fast as Cathie. If it takes them 60 min to paint a living room with all 3 working together, how long would it take Abbie if she works alone?

    So far this is what I got:

    Rate Distance Time
    Cathies 3x 1 1/3x
    Beth 2x 1 1/2x
    Abbie x 1 1/x

    I then did (1/2x)+(1/3x)+(1/x)=1

    Can someone explain to me where I keep going wrong? Thanks
    Umm, you used the formula, Distance = Rate * Time here. Very good.
    I use, task = rate *time.

    Abbie paints twice as fast as Beth and three times as fast as Cathie.
    Let A = rate of Abbie painting alone
    And B = rate of Beth painting alone
    And C = rate of Cathie painting alone

    So,
    A = 2B -----(i)
    so,
    B = A/2

    A = 3C ----(ii)
    so,
    C = A/3

    If it takes them 60 min to paint a living room with all 3 working together,
    Rate *time = distance
    (A +B +C)(60min) = 1 complete job
    (A +A/2 +A/3)(60) = 1
    60A +30A +20A = 1
    110A = 1
    A = 1/110 job/min -----rate of Abbie working alone.

    It means Abbie can finish the job, working alone, in 110 minutes. ----answer.

    Check,
    Distance = Rate *Time
    1 = A *110
    A = 1/110 -------------OK.

    Check,
    A = 1/110
    B = A/2 = 1/220
    C = A/3 = 1/330

    Distance = Rate *time
    1 =? (A +B +C)(60)
    1 =? (1/110 +1/220 +1/330)(60)
    1 =? [(6 +3 +2)/660](60)
    1 =? [11/660](60)
    1 =? 660/660
    1 =? 1
    Yes, so, OK.
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