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Math Help - More help with quadratic equation word problems...

  1. #1
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    More help with quadratic equation word problems...

    Sorry for posting two threads but I can't seem to figure these out.

    1)An express train makes the run between two cities 250km apart in 1.25h less than a local train whose speed is 10km/h less. Find the average speed of the express

    2)A farmer has a rectangular field 400m by 500m. On this field a uniform strip on the outside will be left unplanted so that half of the total area will be planted. How wide is the strip?

    Thanks so much to whoever took the time to read these
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by stephie View Post
    1)An express train makes the run between two cities 250km apart in 1.25h less than a local train whose speed is 10km/h less. Find the average speed of the express
    Let the speed of the express be e, and log the local train be s.

    The time that the express takes is t_e = 250/e, and the time the local train takes is t_s = 250/s. As s = e - 10 we are left with:

    t_e = 250/e,

    and

    t_s = 250/(e-10).

    We are also told that:

    t_e = t_s - 1.25,

    so we have:

    250/e = 250/(e-10) - 1.25.

    Multiply through by e(e-10) to get:

    250 (e-10) = 250 e - 1.25 e (e-10)

    which simplifies to the quadratic:

    1.25 e^2 - 12.5 e - 2500 = 0,

    which has roots e=50 and e=-40, but as e should be positive we find
    e=50.

    RonL
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  3. #3
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    Quote Originally Posted by stephie View Post
    ...
    2)A farmer has a rectangular field 400m by 500m. On this field a uniform strip on the outside will be left unplanted so that half of the total area will be planted. How wide is the strip?...

    Hello, stephie,

    I've attached a diagram of the field.

    Let x be the width of the strip with 0 ≤ x ≤ 200. Then the area of the strip is:
    4x at the 4 corners
    2*x(500 - 2x) two rectangles at the longer sides of the field
    2*x(400 - 2x) two rectangles at the shorter sides of the field

    4x + 2*x(500 - 2x) + 2*x(400 - 2x) = *400*500

    4x + 1000x - 4x + 800x - 4x = *400*500

    -4x + 1800x - 100,000 = 0. Solve the quadratic equation for x:

    x = 225 25*√(41)

    x ≈ 385.08 m (this value doesn't belong to the domain) or x ≈ 64.92 m

    EB
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