One conveyor belt can move 1000 boxes in 9 minutes. Another can move 1000 boxes in 11 minutes. If another conveyor belt is added and all thr

Question

One conveyor belt can move 1000 boxes in 9 minutes. Another can move 1000 boxes in 11 minutes. If another conveyor belt is added and all three are used, the boxes are moved in 3 minutes. How long would it take the third conveyor belt alone to do the same job?

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Nevaeh 15 hours 2021-10-12T08:52:12+00:00 1 Answer 0

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    2021-10-12T08:53:26+00:00

    Answer:

    It would take 7.62 minutes for the third conveyor belt alone to do the same job

    Step-by-step explanation:

    The together rate is the sum of each separate rate.

    In this question:

    First conveyor: Rate of 1/9.

    Second: Rate of 1/11.

    Third: Rate of 1/x.

    Total: 1/3

    So

    \frac{1}{9} + \frac{1}{11} + \frac{1}{x} = \frac{1}{3}

    \frac{11x + 9x + 99}{99x} = \frac{1}{3}

    \frac{20x + 99}{99x} = \frac{1}{3}

    3(20x + 99) = 99x

    60x + 297 = 99x

    39x = 297

    x = \frac{297}{39}

    x = 7.62

    It would take 7.62 minutes for the third conveyor belt alone to do the same job

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