Results 1 to 4 of 4

Math Help - solving equations in English

  1. #1
    Member
    Joined
    Sep 2006
    Posts
    99

    solving equations in English

    Systems of equations can be easily solved through the matrix. But when English is used, the difficulty of the problem is compounded. I am stumped by this question, I cannot figure out how to solve this question. Please help.

    Jack drives from her country home to the city, a distance of 380 km. He drives part of the way on back roads, at an average speed of 50 km/h, and part on highways, at an average speed of 100 km/h. The trip takes 5 hours. How far does he drive on each type of road?

    Answer key: 260 km on highways, 120 km on back roads

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by shenton View Post
    Systems of equations can be easily solved through the matrix. But when English is used, the difficulty of the problem is compounded. I am stumped by this question, I cannot figure out how to solve this question. Please help.

    Jack drives from her country home to the city, a distance of 380 km. He drives part of the way on back roads, at an average speed of 50 km/h, and part on highways, at an average speed of 100 km/h. The trip takes 5 hours. How far does he drive on each type of road?

    Answer key: 260 km on highways, 120 km on back roads

    Thanks.
    Translate this into an equation. Let x \mbox{ km} be the distance travelled on back roads. Then 380-x\mbox{ km} is the distance travelled on highways. Then the time taken is:

    t=x/50+(380-x)/100=5 \mbox{ hours}

    Now solve this equation for x.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,659
    Thanks
    600
    Hello, shenton!

    I use baby-talk with such word problems . . . it works for me.


    Jack drives from her country home to the city, a distance of 380 km.
    He drives part of the way on back roads, at an average speed of 50 km/h,
    and part on highways, at an average speed of 100 km/h.
    The trip takes 5 hours.
    How far does he drive on each type of road?

    Answer key: 260 km on highways, 120 km on back roads

    There are a number of approaches to this problem.
    If you prefer a system of equations, we can do it like this . . .

    Let x = number of km on back roads.
    Let y = number of km on highways.
    . . We know that: . x + y \:=\:380 (1)

    He drove x km at 50 km/hr.
    . . This took him \frac{x}{50} hours.
    He drove y km at 100 km/hr.
    . . This took him \frac{y}{100} hours.
    Since his total time was 5 hours, we have: . \frac{x}{50} + \frac{y}{100} \:=\:5
    . . Multiply by 100: . 2x + y \:=\:500 (2)


    Solve the system of equations: . \begin{array}{cc}(1) \\ (2) \end{array}\begin{array}{cc} x + y & =\:380 \\ 2x + y & =\:500\end{array}

    Subtract (1) from (2): . \boxed{x \,= \,120}

    Substitute into (1): . 120 + y\:=\:380\quad\Rightarrow\quad\boxed{y \,=\,260}


    Therefore, Jack drove: . \begin{array}{cc} 120\text{ km} & \text{on back roads} \\ 260\text{ km} & \text{on highways}\end{array}

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Sep 2006
    Posts
    99
    Thanks, Soroban for showing the 2 equations and the detailed workings.

    This question and the quarters and dimes questions are one of the most difficult word problems.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: November 30th 2011, 01:41 AM
  2. English to Proposition Statements
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: January 19th 2011, 11:40 PM
  3. Replies: 5
    Last Post: October 30th 2010, 11:47 AM
  4. Translating English to FO Logic
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: August 3rd 2010, 06:32 AM
  5. Maths and English
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 20th 2009, 06:48 AM

Search Tags


/mathhelpforum @mathhelpforum