Working together, two secretaries can stuff the envelopes for a political fund-raising letter in 3 hours. Working alone, it takes the slower

Question

Working together, two secretaries can stuff the envelopes for a political fund-raising letter in 3 hours. Working alone, it takes the slower worker 8 hours longer to do the job than the faster worker. How long does it take each to do the job alone?

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Ximena 2 weeks 2021-09-09T10:45:08+00:00 1 Answer 0

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    2021-09-09T10:46:15+00:00

    Answer:

    Faster worker takes 4 hours and slower worker takes 12 hours.

    Step-by-step explanation:

    Let x be the time ( in hours ) taken by faster worker,

    So, according to the question,

    Time taken by slower worker = (x+8) hours,

    Thus, the one day work of faster worker = \frac{1}{x}

    Also, the one day work of slower worker = \frac{1}{x+8}

    So, the total one day work when they work together = \frac{1}{x}+\frac{1}{x+8}

    Given,

    They take 3 hours in working together,

    So, their combined one day work = \frac{1}{3}

    \implies \frac{1}{x}+\frac{1}{x+8}=\frac{1}{3}

    \frac{x+8+x}{x^2+8x}=\frac{1}{3}  ( Adding fractions )

    3(2x+8)=x^2+8x    ( Cross multiplication )

    6x+24=x^2+8x       ( Distributive property )

    x^2+2x-24=0          ( Subtraction property of equality )

    By quadratic formula,

    x=\frac{-2\pm \sqrt{100}}{2}

    x=\frac{-2\pm 10}{2}

    \implies x=4\text{ or }x=-6

    Since, hours can not negative,

    Hence, time taken by faster worker = x hours = 4 hours,

    And, the time taken by slower worker = x + 8 = 12 hours.

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