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4 May, 01:51

Two companies working together can clear a parcel of land in 24 hours. Working alone, it would take Company A 10 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. 4 May, 04:06
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    43 hours 31 minutes

    Step-by-step explanation:

    Let the time it takes Company B=x

    Company B's Work Rate=1/x

    It would take Company A 10 hours longer, Time for A=x+10

    Company A's Work Rate=1 / (x+10)

    The two companies working together can clear a parcel of land in 24 hours.

    Their joint work rate=1/24

    Therefore:

    1/x + 1 / (x+10) = 1/24

    Taking L. C. M

    (x+10+x) / (x (x+10)) = 1/24

    (2x+10) / (x²+10x)) = 1/24

    On Cross multiplication

    24 (2x+10) = x²+10x

    48x+240=x²+10x

    x²+10x-48x-240=0

    x²-38x-240=0

    x = - 5.52 or 43.52

    Since x>0

    x = 43.52 hours

    = 43 hours 31 minutes

    It would take Company B 43 hours 31 minutes to clear the parcel of land.
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