Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By Qwob

Math Help - Quadratic Formula Question #5

  1. #1
    Member
    Joined
    Feb 2013
    From
    Canada
    Posts
    131

    Post Quadratic Formula Question #5

    http://i.imgur.com/TeW1TELh.jpg

    I'm not sure how to do these word questions...

    My attempt:

    150x + 200x - 600 = 0

    I suck at this, any help would be great! Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Sep 2011
    From
    UK
    Posts
    17
    Thanks
    7

    Re: Quadratic Formula Question #5

    Think as travelling north as travelling in the y-plane, and travelling west as in the x-plane.

    speed = \frac {distance}{time}

    (or more correctly)

    velocity = \frac{displacement}{time}

    After 2 hours, the first plane will have travelled 300km. (150x2)

    We can model this as y = 300 + 150t, where t is the time in hours

    After 2 hours, second plane will have just taken off and therefore travelled 0km.

    We can model this as x = 200t, where t is the time in hours.

    Now, think of this as a vector triangle question like in physics. This way we have a right-angled triangle, and we want the hypotenuse (the distance between the two planes) to be 600km.

    Therefore we have:

    x^2 + y^2 = 600^2

    (200t)^2 + (300 + 150t)^2 = 600^2

    Now we solve for t:

    40000t^2 + 90000 + 90000t + 22500t^2 = 360000

    simplifying:

    400t^2 + 900 + 900t + 225t^2 = 3600

     80t^2 + 180 + 180t + 45t^2 = 720

    125t^2 + 180t - 540 = 0

    25t^2 + 36t - 108 = 0

    Using a calculator to quickly solve the quadratic:

    t = 1.48 hours or t = -2.92 hours

    since t cannot be negative, t must be 1.48 hours (or 1.5 hours to the nearest tenth of an hour).

    This is just a solution to the problem. There may (and hopefully should) be a much easier way to solve it, maybe given as an example somewhere in your book. If not, I hope this helps.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Quadratic Formula Question #3
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: May 6th 2013, 06:39 PM
  2. Quadratic Formula Question #4
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 6th 2013, 10:48 AM
  3. quadratic formula question
    Posted in the Algebra Forum
    Replies: 5
    Last Post: May 8th 2012, 05:11 PM
  4. Question: Quadratic Formula
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 19th 2010, 01:59 PM
  5. Quadratic formula question
    Posted in the Algebra Forum
    Replies: 4
    Last Post: March 21st 2008, 03:37 PM

Search Tags


/mathhelpforum @mathhelpforum