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4 July, 04:32

It takes 36 minutes to manually package 400 candles into boxes for shipment. When an automated packaging system works together with the manual packaging system, 400 candles can be boxed in 9 minutes. How many minutes are required for the automated packaging system working alone to box 400 candles?

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  1. 4 July, 07:56
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    12 minutes

    Step-by-step explanation:

    Candles can be manually packed at the rate of ...

    ... (400 candles) / (36 minutes) = 11 1/9 candles/minute

    The two systems together pack candles at the rate of ...

    ... (400 candles) / (9 minutes) = 44 4/9 candles/minute

    Then the machine's packing rate is the difference between the total and the manual rates:

    ... machine rate = (44 4/9 candles/minute) - (11 1/9 candles/minute)

    ... = 33 1/3 candles/minute.

    At this rate, the machine working alone can pack 400 candles in ...

    ... (400 candles) / (33 1/3 candles/minute) = (400 / (100/3)) minutes

    ... = 400 * 3/100 minutes = 12 minutes
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