Results 1 to 3 of 3

Math Help - need help setting up a uniform motion problem

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    1

    need help setting up a uniform motion problem

    I can't figure out how to set this up. Would someone help please.

    Two cars enter the florida turnpike at Commercial Blvd. at 8am each heading toward Wildwood. One cars average speed is 10mph more than the other's. The faster car arrives at Wildwood at 11am, 1/2 hour before the other car. What is the average speed of each car? How far did each travel?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by dsgarr View Post
    I can't figure out how to set this up. Would someone help please.

    Two cars enter the florida turnpike at Commercial Blvd. at 8am each heading toward Wildwood. One cars average speed is 10mph more than the other's. The faster car arrives at Wildwood at 11am, 1/2 hour before the other car. What is the average speed of each car? How far did each travel?
    ok, so you should know that

    \text{Average Speed} = \frac {\text{Total distance traveled}}{\text{Total time taken}}

    Here, the total time for the faster car 3 hrs. the total time for the slower car is 3.5 hrs.

    Now, let the average speed of the faster car be v, then the average speed of the slower car is (v - 10).

    also, they travel the same distance, d, which is yet an unknown.

    so, we have:

    v = \frac d3 ...........................(1) this is for the faster car

    and

    v - 10 = \frac d{3.5} ..............(2) this is for the slower car

    you have two equations and two unknowns, all you want to find is v and you will know the average speed of the faster car, and hence, by subtracting 10, the average speed of the slower car
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,550
    Thanks
    542
    Hello, dsgarr!

    Two cars enter the florida turnpike at Commercial Blvd. at 8am, each heading
    toward Wildwood. One car's average speed is 10mph more than the other's.
    The faster car arrives at Wildwood at 11am, 1/2 hour before the other car.
    What is the average speed of each car? How far did each travel?

    Let x = speed of the slower car.
    Let x+10 = speed of the faster car.

    Let D = distance to Wildwood.


    The faster car reached Wildwood in 3 hours.
    . . Its time is: . \frac{D}{x+10} hours.
    We have: . \frac{D}{x+10} \:=\:3 \quad\Rightarrow\quad D \:=\:3x + 30 .[1]


    The slower car reached Wildwood in 3.5 hours.
    .Its time is: . \frac{D}{x} hours.
    We have: . \frac{D}{x} \:=\:\frac{7}{2} \quad\Rightarrow\quad D \:=\:\frac{7}{2}x .[2]


    Equate [2] and [1]: . \frac{7}{2}x \:=\:3x + 30 \quad\Rightarrow\quad \frac{1}{2}x \:=\:30 \quad\Rightarrow\quad x \:=\:60

    Substitute into [2]: . D \:=\:\frac{7}{2}(60) \:=\:210


    The slower car went 60 mph; the faster car went 70 mph.

    The distance to Wildwood is 210 miles.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Uniform Accelerated Motion
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 16th 2011, 05:11 PM
  2. Uniform Circular Motion Problem
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: February 28th 2010, 11:30 AM
  3. Uniform motion & Inequalities
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 18th 2010, 12:03 PM
  4. Motion with Uniform Acceleration
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: October 4th 2009, 05:08 AM
  5. Uniform Circular Motion
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 18th 2008, 02:30 PM

Search Tags


/mathhelpforum @mathhelpforum