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6 April, 12:49

Two companies working together can clear a parcel of land in 27 hours. Working alone, it would take Company a 2 hours longer to clear the land than it would Company B. How long would it take Company B to clear the parcel of land alone?

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  1. 6 April, 13:05
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    53 hours

    Step-by-step explanation:

    If A is the time it takes Company A, and B is the time it takes Company B, then:

    1/27 = 1/A + 1/B

    A = B + 2

    Substitute and solve:

    1/27 = 1 / (B + 2) + 1/B

    1/27 = (B + B + 2) / (B (B + 2))

    1/27 = (2B + 2) / (B² + 2B)

    27 (2B + 2) = B² + 2B

    54B + 54 = B² + 2B

    0 = B² - 52B - 54

    B = [ - (-52) ± √ ((-52) ² - 4 (1) (-54)) ] / 2 (1)

    B = (52 ± √2920) / 2

    B ≈ 53.0

    It would take Company B approximately 53 hours.
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