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March 30, 2017

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Mattie Evans drove 250 miles in the same amount of time that it took a turbopropeller plane to travel 1250 miles. The speed of the plane was 200 mph faster than the speed of the car. Find the speed of the plane

  • Algebra - ,

    its 450 mph

  • Algebra - ,

    Speed = distance/time

    time = distance/speed

    Let x = plane speed and y = driving speed

    y = x + 200

    250/x = 1250/y

    Substitute x + 200 for y in second equation and solve for x. Insert that value into the first equation and solve for y. Check by inserting both values into the second equation.

  • Algebra - ,

    Car speed = X-mi/h,
    Plane speed = (X + 200) mi/h,

    Eq1: d1 = X*t = 250 mi,
    t = 250 / X,

    Eq2: d2 = (X + 200)t = 1250 mi.

    Substitute 250 / X for t in Eq2:
    (X + 200)250/X = 1250,
    250 + 50000/X = 1250,
    50000 / X = 1250 - 250,
    50000 / X = 1000,
    Cross multiply:
    1000X = 50000,

    X = 50000 / 1000 = 50 mi/h = car speed.
    (X + 200) = 250 mi/h = plane speed.

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