Results 1 to 3 of 3

Math Help - Applying Cramer's Rule to Word Problems

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    4

    Question Applying Cramer's Rule to Word Problems

    I've spent all weekend trying to figure this out, and I believe I'm overthinking the problem and the answer might be staring me in the face.

    My instructions for the following word problem are to set up an appropriate system of two linear equations in two unknowns and then solve the system by determinants.

    The problem is:

    Two joggers are 2.0 mi apart. If they jog toward each other, they will meet in 12 minutes. If they jog in the same direction, the faster one will overtake the slower one in 2.0 hours. At what rate does each jog?

    I am not necessarily looking for the final answer to this problem, I'd just like some help on how the two equations should be set up. Especially regarding jogging in the same direction using only two unknowns.

    Please help me!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    A is 2mi away from B

    Let r = rate of A
    And s = rate of B
    And, say, r is faster than s.

    Be consistent with units.
    units for distance is mi.
    units for time is hr.
    units for rate in mi/hr.
    So, 12 minutes = 12/60 = 1/5 hr

    distance = rate * time

    They jog toward each other
    r(1/5) +s(1/5) = 2
    So,
    r +s = 10 -------------(1)

    They jog in the same direction
    (distance traveled by A) = (2 mi. + distance traveled by B)
    r(2.0) = 2 +s(2.0)
    2r = 2 +2s
    r = 1 +s
    r -s = 1 ---------(2)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    4
    It seems so simple now!

    I was confusing myself by trying to convert hours into minutes first, instead of vice versa.

    Thank you!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. cramer rule
    Posted in the Algebra Forum
    Replies: 4
    Last Post: December 11th 2009, 08:22 PM
  2. Word Problem Using Cramer's Rule
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: April 9th 2009, 12:42 PM
  3. Applying the power rule to problems
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 23rd 2009, 03:02 PM
  4. Cramer's Rule
    Posted in the Algebra Forum
    Replies: 6
    Last Post: January 3rd 2009, 08:43 AM
  5. Cramer's Rule
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 23rd 2008, 06:23 PM

Search Tags


/mathhelpforum @mathhelpforum