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Math Help - Average/Rate/Time Word Problem.

  1. #1
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    Average/Rate/Time Word Problem.

    The problem reads, If Art and Rita can do a job in four 4 hours when workin gtogether at their respective constant rates and Art can do the job alone in 6 hours, in how many hours can Rita do the job alone?

    The problem is set up like this:

    1/6 +1/R = 1/4

    (R+6)/(6R) = 1/4

    4R + 24 = 6R

    R = 12

    I totally understand how the problem is setup, but do not understand where the (R+6)/(6R) comes from? Then, I am totally in the dark as to how (R+6)/(6R) = 1/4 could work out to 4R + 24 = 6R!

    Any, and I do mean ANY, help on this one would be great. I feel retarded because this one is so simple I do not know why I cannot figure it out.

    Thanks!
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  2. #2
    Member anonimnystefy's Avatar
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    Re: Average/Rate/Time Word Problem.

    you do this by finding the lcm(lowest common multiple) of 6 and R which is 6R:
    1/6 +1/R = 1/4

    R/6R +6/6R=1/4

    (R+6)/6R=1/4

    Next you multiply the whole equation by 24R which is a common multiple of 6R and 4:
    (R+6)/6R=1/4

    24R(R+6)/6R=24R/4

    4(R+6)=6R

    4R+24=6R

    24=2R

    R=12

    the whole thing could have been done this way:
    1/6 +1/R = 1/4
    1/R=1/4-1/6
    1/R=6/24-4/24
    1/R=2/24
    1/R=1/12
    R=12
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  3. #3
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    Re: Average/Rate/Time Word Problem.

    Quote Originally Posted by Stoneface View Post
    The problem reads, If Art and Rita can do a job in four 4 hours when workin gtogether at their respective constant rates and Art can do the job alone in 6 hours, in how many hours can Rita do the job alone?

    The problem is set up like this:

    1/6 +1/R = 1/4

    (R+6)/(6R) = 1/4

    4R + 24 = 6R

    R = 12

    I totally understand how the problem is setup, but do not understand where the (R+6)/(6R) comes from? Then, I am totally in the dark as to how (R+6)/(6R) = 1/4 could work out to 4R + 24 = 6R!

    Any, and I do mean ANY, help on this one would be great. I feel retarded because this one is so simple I do not know why I cannot figure it out.

    Thanks!
    \frac{1}{6}+\frac{1}{R}=\frac{1}{4}

    ADDING FRACTIONS: Needs to have a common denominator.
    (\frac{R}{R}\cdot\frac{1}{6})+(\frac{1}{R}\cdot \frac{6}{6})=\frac{1}{4}

    \frac{R}{6R}+\frac{6}{6R}=\frac{1}{4}


    \frac{R+6}{6R}=\frac{1}{4}

    Clearing Fractions.

    6R\cdot\frac{R+6}{6R}=\frac{1}{4}\cdot6R

    Clearing Fractions.

    4\cdot{(R+6)}=\frac{6R}{4}\cdot4

    4R+24=6R

    Now Solve for R and complete.
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