Results 1 to 2 of 2

Math Help - Calculus optimization

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    38

    Calculus optimization

    A train leaves the station at 10:00 and travels due north at a speed of 60 km/h. Another train has been heading due west at 45 km/h and reaches the same station at 11:00. At what time were the two trains closest together?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Mar 2009
    Posts
    35
    Thanks
    1
    An actual train queastion. And here I thought they were just a tv trope.

    Train 1 distance from station is 60t Where t=0 at 10
    Train 2 distance from station is 45-45t
    Pythagorean theorem gives us the distance between trains:
    sqrt ((60t)^2 + (45-45t)^2)
    The square root has a minimum at the same time as its contents so we can ignore its leaves us with finding the minimum of
    5625t^2 - 4050T +2025
    Differentiating to find the minimum gives us
    11250t - 4050 = 0 or t=.36
    Multiply by 60 to get 21.6 minutes after 10
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. calculus Optimization problem help
    Posted in the Calculus Forum
    Replies: 0
    Last Post: August 10th 2010, 09:36 PM
  2. Calculus-Optimization
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 21st 2008, 07:35 PM
  3. AP Calculus-Optimization
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 3rd 2007, 01:55 AM
  4. Calculus Optimization
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 12th 2007, 02:43 PM
  5. [SOLVED] Optimization and calculus
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 13th 2005, 11:29 PM

Search Tags


/mathhelpforum @mathhelpforum