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22 April, 03:14

Two constructors working together finished building a room in 6 days. how long would it take for each constructor to build the room by himself, if it is known that one of them would require 9 more days than the other?

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  1. 22 April, 04:58
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    It would take one construction worker 9 days and the other 18 days.

    Let x be the number of days the first construction worker takes to build the room by himself. If x were 2, he could build 1/2 of the room in the time limit, etc ... so 1/x will be the portion of the room he can build by himself in the given tie limit.

    The second construction worker can build 1 / (x+9) of the room by himself in the given time limit.

    Together, we have the equation

    1/x (6) + 1 / (x+9) (6) = 1

    [The speed of the first contractor times the number of days, and the speed of the second contractor times the number of days; together they build 100% of the room]

    This gives us

    6/x + 6 / (x+9) = 1

    We will multiply everything by x to get it off of the denominator:

    6/x (x) + (6 / (x+9)) (x) = x

    6 + 6x / (x+9) = x

    Multiply everything by x+9 now:

    6 (x+9) + (6x / (x+9)) (x+9) = x (x+9)

    6x + 54 + 6x = x² + 9x

    12x + 54 = x² + 9x

    Subtract 12x from each side:

    12x + 54 - 12x = x²+9x-12x

    54 = x²-3x

    Subtract 54 from each side:

    54-54 = x²-3x-54

    0 = x²-3x-54

    This factors easily; - 9 (6) = - 54 and - 9+6 = - 3:

    0 = (x-9) (x+6)

    Using the zero product property we know either x-9=0 or x+6=0; this gives us x=9 or x=-6. Negative time makes no senses, so x=9 hours.

    This means the slower contractor takes 9+9 = 18 hours.
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