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Algebra..please check my work!!

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At 3 p.m., Brunhilde headed north at 30 kilometers per hour. Two hours later Ludwig headed south at 40 kilometers per hour. At what time will they be 340 kilometers apart?

I know that the distance from Brunhilde(Db) plus the distance from Ludwig(Dl) is equal to 340, which is translated as (Tb)(Rb)+(Tl)(Rl)=340, "T" standing for time, and "R" standing for rate...so I substitue in the rates to get 40Tb + 30Tl=340, but the answer is wrong..the book has it as 9 p.m....what am I doing wrong!!!!?

  • Algebra..please check my work!! - ,

    They separate at a rate of 30 + 40 =
    70 km/hr, since they are going in opposite directions. It takes 340/70 = 4.857 hours to become 340 km apart. That would be at 8:51 PM, since 0.857 x 60 = 51+ minutes. Are you sure they didn't ask for the time when they are 350 km apart, not 340? Then the answer would be exactly 9 PM

  • Algebra..please check my work!! - ,

    Yea the answer in the back of the book has it at 9 p.m. ,and yea they do ask for the time when their 340 kilometers apart, interesting, could the book be wrong?lol

  • Algebra..please check my work!! - ,

    When you divided 340/70 and came up with 4.857, how'd you come up with 8?

  • Algebra..please check my work!! - ,

    The book is correct.

    Let the time passed after Ludwig left be t hours, remember he left 2hours after her, so she already went 60 km

    So the distance that Brunhilde went is 60+30t
    and the distance that Ludwig went is 40t
    so....
    60 + 30t + 40t = 340
    70t = 280
    t = 4

    So they are 340 km apart 4 hours after Ludwig left, but he left at 5 pm, so they are apart 340 km at 9 pm

  • Algebra..please check my work!! - ,

    Sorry; I misread the problem and neglected the time delay

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