Results 1 to 4 of 4

Math Help - Quadratic Equation!?

  1. #1
    Newbie
    Joined
    May 2010
    From
    Liverpool
    Posts
    16

    Red face Quadratic Equation!?

    Hi there,

    I had the following question in a exam a couple of days ago and I couldn't solve it, but I know I had to use a Quadratic Equation (ax+bx+c). Still I didn't came up with a formula....

    Question:
    A journey from A to B is 550km. In my steady little car that travels at a nice sedate speed I get there in a reasonable time. However if I hired something more up market that travels on average 6km/hr faster (still keeping under the speed limit of course), I can get to B 50 minutes sooner.

    Determine the average speed of my steady little car, and how long I will take to get to B.

    Thank you for your help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by MickG86 View Post
    Hi there,

    I had the following question in a exam a couple of days ago and I couldn't solve it, but I know I had to use a Quadratic Equation (ax+bx+c). Still I didn't came up with a formula....

    Question:
    A journey from A to B is 550km. In my steady little car that travels at a nice sedate speed I get there in a reasonable time. However if I hired something more up market that travels on average 6km/hr faster (still keeping under the speed limit of course), I can get to B 50 minutes sooner.

    Determine the average speed of my steady little car, and how long I will take to get to B.

    Thank you for your help
    Hi, MickG86,

    In general,

    x = v_{av}t

    So, let v_s represent the slower speed, and v_f represent the faster one, likewise t_s and t_f. We have

    x = v_st_s
    x = v_ft_f = (v_s+6)(t_s-5/6)

    Set them equal

    v_st_s = (v_s+6)(t_s-5/6)

    Solve for t_s with the intent of substituting later on

    v_st_s = v_st_s-(5/6)v_s+6t_s-5

    6t_s = (5/6)v_s+5

    t_s = (5/36)v_s+5/6

    Substitute

    x = v_st_s

    x = v_s((5/36)v_s+5/6)

    36x = v_s(5v_s+30)

    36x = 5v_s^2+30v_s

    5v_s^2+30v_s - 36x = 0

    5v_s^2+30v_s - 36(550) = 0

    v_s^2+6v_s - 3960 = 0

    Quadratic equation... (I'll leave that part to you)

    Solution: v_s = 60 \text{ km/h}

    Plug it back into

    x = v_st_s

    to get

    t_s = 9 \text{ hrs}, 10 \text{ min}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,110
    Thanks
    68
    Code:
    [1] A ....@ v ..........[550].............. B : h hours
     
    [2] A ....@ v+6 ........[550].............. B : h-5/6 hours
    [1] hv = 550
    [2] (h-5/6)(v+6) = 550
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2010
    From
    Liverpool
    Posts
    16

    Thumbs up

    Thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Quadratic Equation
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 30th 2010, 10:46 AM
  2. Replies: 3
    Last Post: April 25th 2010, 03:53 PM
  3. Quadratic Equation
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 14th 2009, 05:34 AM
  4. Quadratic Equation
    Posted in the Algebra Forum
    Replies: 4
    Last Post: August 11th 2009, 10:11 AM
  5. Quadratic Equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 1st 2007, 01:06 AM

Search Tags


/mathhelpforum @mathhelpforum