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Systems of Equations: Word Problem

  1. Feb 21, 2012 #1

    S.R

    User Avatar

    1. The problem statement, all variables and given/known data
    A small plane flying into the wind takes 3 h 20 min to complete a flight of 960km. Flying with the wind, the same plane takes 2 h 30 mins to make the trip. What is the speed of the plane? What is the speed of the wind?


    2. Relevant equations
    N/A

    3. The attempt at a solution
    I'm unsure on how to set-up the two equations:

    Let x represent the speed of the plane and y represent the speed of the wind.

    7/3(x-y)=960

    5/2(x+y)=960

    Is this representation correct?
     
  2. jcsd
  3. Feb 21, 2012 #2

    Mark44

    Staff: Mentor

    Looks good to me. Now solve for x and y.
     
  4. Feb 21, 2012 #3

    S.R

    User Avatar

    EDIT: The mistake is 7/3; it is suppose to be 10/3.

    Rewriting:

    10x-10y=2880

    5x+5y=1920

    or

    5x-5y=1440

    5x+5y=1920

    10x=3360

    x=336

    Substituting:

    5(336)+5y=1920

    1680+5y=1920

    y=48
     
    Last edited: Feb 21, 2012
  5. Feb 21, 2012 #4

    Mark44

    Staff: Mentor

    Sorry, I didn't notice before, but 3hr 20 min = 10/3 hr, not 7/3 hr.
     
  6. Feb 21, 2012 #5

    S.R

    User Avatar

    Thanks :smile:.
     
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