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29 March, 13:40

Mrs. hensen cataloged a group of incoming library books in 8 hours. mr. taylor can catalog the same number of books in 4 hours. mrs. phillips can catalog them in 6 hours. how long would it take if they all worked together?

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  1. 29 March, 14:23
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    Let n = the number of books.

    Mrs. Hensen's working rate is

    x = n/8 books/h

    Mr. Taylor's working rate is

    y = n/4 books/h

    Mrs. Phillip's working rate is

    z = n/6 books/h

    When they work together, they can catalog n books in

    (n books) / (x+y+z books/h)

    = n / (n/8 + n/4 + n/6)

    = 1 / (1/8 + 1/4 + 1/6)

    = 1 / (13/24)

    = 24/13 hours

    The time required is 24/13 h = 1.8462 h = 1 hour, 51 min

    Answer: 1.8462 hours (or 1 hour, 51 minutes)
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