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college algebra

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to travel 132 miles it take sue riding a moped 2 hours less time then it takes doreen to travel 56 miles riding a bike. sue travels 15 miles per hour faster then doreen find the time and rates

  • college algebra - ,

    Doreen's speed = X mi/h
    Doreen's time = Y hrs(d = 56mi).
    Eq1: X*Y = 56.
    Y = 56/X

    Sue's speed = (X+15) mi/h.
    Sue's time = (Y-4) hrs(d = 132mi).
    Eq2: (X+15)(Y-4) = 132.

    In Eq2, substitute 56/X for Y:
    (X+15)(56/X-4) = 132
    56-4x+840/x-60 = 132
    -4x+840/x-4 = 132
    Multiply both sides by X:
    -4x^2+840-4x = 132x
    -4x^2-136x+840 = 0
    Divide both sides by -4:
    x^2+34x-210 = 0.
    Use Quad. formula.
    X = 5.34 mi/h = Doreen's speed.
    X+15 = 5.34+15 = 20.34 mi/h=Sue's speed.

    Y = 56/X = 56/5.34 = 10.5 h. = Doreen's
    time.
    Y-4 = 10.5-4 = 6.5 hrs = Sue's hrs.

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