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dreamv Rising GMAT Star Default Avatar
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work order Post Tue Feb 21, 2012 3:43 pm
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    Working alone at its own constant rate, a machine seals K cartons in 8 hours, and working alon at its own constant rate, a second machine seals K cartons in 4 hours. If the two machines, each working at its won constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

    A. 25%
    B. 33 and 1/3 %
    C. 50%
    D. 66 and 2/3 %
    E. 75%

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    pemdas GMAT Titan Default Avatar
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    Post Tue Feb 21, 2012 4:09 pm
    two machines, X and Y
    their speeds, X speed 1/8 and Y speed 1/4 (the speed of Y greater)
    combined speed by X&Y will be (1/4 +1/8)=3/8
    find the required, i.e. ratio faster speed machine(Y)/combined speed machines(X&Y)=1/4 : 3/8=1/4 *8/3=2/3 or 66%
    d
    dreamv wrote:
    Working alone at its own constant rate, a machine seals K cartons in 8 hours, and working alon at its own constant rate, a second machine seals K cartons in 4 hours. If the two machines, each working at its won constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

    A. 25%
    B. 33 and 1/3 %
    C. 50%
    D. 66 and 2/3 %
    E. 75%

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    Post Tue Feb 21, 2012 5:33 pm
    dreamv wrote:
    Working alone at its own constant rate, a machine seals K cartons in 8 hours, and working alon at its own constant rate, a second machine seals K cartons in 4 hours. If the two machines, each working at its won constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

    A. 25%
    B. 33 and 1/3 %
    C. 50%
    D. 66 and 2/3 %
    E. 75%
    The slower machine takes TWICE AS LONG to produce K cartons.
    TWICE AS LONG means HALF AS FAST.
    Thus, for every 2 cartons produced by the faster machine, the slower machine produces 1 carton.
    Thus, of every 3 cartons produced, the fraction produced by the faster machine = 2/3 = 66 2/3%.

    The correct answer is D.

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