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18 January, 05:45

It takes Shawn 2 more hours to stain a deck than Michelle. Together it takes them 2.4 hours to complete the work. How long would it take Shawn to stain the deck by himself?

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  1. 18 January, 05:48
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    Answer: 6 hours

    Step-by-step explanation:

    Shawn's time = Ts

    Michele's time = Tm

    But Tm + 2hours = Ts

    Time here is expressed according to work done, their time rate of work can be given by:

    r = Wd/T (where r is the rate of work per time, Wd is work done and T is time spent)

    Since the amount of work is the same for both of them, their rate of work together is given by

    Wd/Tt = Wd/Tm + Wd/Ts

    Since Wd is the same across board, we can eliminate Wd, leaving us with:

    1/Tt = 1/Tm + 1/Ts (Tt represents the time they both expended in doing the work together

    Tt = 2.4 hours

    Therefore,

    1/2.4 = 1/Tm + 1/Ts

    Taking the LCM of the left hand side fraction

    1/2.4 = (Ts + Tm) / TmTs

    We cross multiply

    2.4Ts + 2.4Tm = TmTs ...

    Remember, Ts = (Tm + 2) hrs

    We substitute for Ts

    2.4 (Tm + 2) + 2.4Tm = Tm (Tm + 2)

    2.4Tm + 4.8 + 2.4Tm = Tm2 + 2Tm

    4.8Tm + 4.8 = Tm2 + 2Tm

    Tm2 - 2.8Tm - 4.8 = 0

    This has become a quadratic equation

    We multiply thought by 10 to make factorization easier

    10Tm2 - 28Tm - 48 = 0

    Then we factorize

    (Tm - 4) (10Tm + 12) = 0

    Tm-4 = 0, Tm = 4hours

    (The other equation (10Tm + 12 = 0) will give a negative result for time, we discard it because it is impossible in these circumstances. We all know that time is a scalar quantity)

    Tm = 4hours (that is Michelle's time)

    Since Tm + 2 = Ts

    (4+2) hours = Ts

    Ts = 6 hours

    Therefore, Shawn will spend 6 hours staining the deck all alone
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