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4 April, 09:04

If patricia were to paint her living room alone, it would take 4 hours. her sister naomi could do the job in 5 hours. how long would it take them working together? if needed, submit your answer as a fraction reduced to lowest terms.

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  1. 4 April, 09:10
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    Practicia completes the job in one hour = 1/4

    Naoimi completes the job in one hour = 1/5

    If Parcticia and Naoimi does it together, let us suppose in x number of hours.

    The equation so form is:

    (1/4) * x + (1/6) * x = 1 (i. e job finished)

    The Least common multiple (LCM) of 4 and 6 = 12

    12 * (1/4) * x + 12 * (1/6) * x = 12*1

    Therefore, solving the equation we get,

    3x + 2x = 12

    5x = 12

    x = 12/5

    x = 2 2/5 hours or 2.24 hours

    Therefore number of hours they took to complete the work is 2 hours and 24 minutes or 2.24 hours.
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