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Math Help - Ambiguous Problem

  1. #1
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    Ambiguous Problem

    Hi Members,
    This is the problem which I didn't understand.
    Miss x walks 35km partly at the rateof 4km/hour and partly at 5km/hour;if she had walked at 5km/hour when she walked at 4km/hour and vice-versa,she would have covered 2 km more in the same time. Find the time she was walking.
    Would any member explain me this problem and how to form simultaneous linear equations?
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  2. #2
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    Re: Ambiguous Problem

    Quote Originally Posted by Vinod View Post
    Hi Members,
    This is the problem which I didn't understand.
    Miss x walks 35km partly at the rateof 4km/hour and partly at 5km/hour;if she had walked at 5km/hour when she walked at 4km/hour and vice-versa,she would have covered 2 km more in the same time. Find the time she was walking.
    Would any member explain me this problem and how to form simultaneous linear equations?
    This is easily set up incorrectly (as I just did and restarted).

    The important thing is that the separate walk times remain fixed.

    From the first statement

    $4 t_1 + 5 t_2 = 35$ and from the second

    $5 t_1 + 4 t_2 = 37$

    or

    $\begin{pmatrix}4 &5 \\ 5 & 4\end{pmatrix}\begin{pmatrix}t_1 \\ t_2\end{pmatrix} = \begin{pmatrix} 35 \\ 37\end{pmatrix}$
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  3. #3
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    Re: Ambiguous Problem

    Hi romsek,
    I have solved  t_{2} = 3 and  t_{1} =5 even before posting this thread but last part of question needs to find out the time she was walking. How is that to be computed?
    Last edited by Vinod; May 13th 2014 at 07:11 AM.
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  4. #4
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    Re: Ambiguous Problem

    What did you choose " t_1" and " t_2" to mean when you set up the problem?
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    Re: Ambiguous Problem

    Quote Originally Posted by Vinod View Post
    Hi romsek,
    I have solved  t_{2} = 3 and  t_{1} =5 even before posting this thread but last part of question needs to find out the time she was walking. How is that to be computed?
    uhh how about $t_1+t_2$
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    Re: Ambiguous Problem

    Quote Originally Posted by HallsofIvy View Post
    What did you choose " t_1" and " t_2" to mean when you set up the problem?
    Solving for $t_1$ and $t_2$ is just like a leap in the dark. It is a shooting of target in the darkness of night.
    So, main question is to find out the time she was walking.
    One point is clear that Miss x walks 35 kms. partly by 4km/hour and partly by 5km/ hour. Other information given in the problem is unclear to me. Do you know the answer?
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  7. #7
    MHF Contributor ebaines's Avatar
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    Re: Ambiguous Problem

    Vinod - you have already figured out that she walked for 5 hours at one speed and 3 hours at another. So the total time she walked was 5 hours + 3 hours=8 hours. It's not ambiguous at all.
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    Re: Ambiguous Problem

    Hi ebaines,
    But the answer provided in the book is 6 hrs 53 minutes 20 seconds. Is that wrong?
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    Re: Ambiguous Problem

    Quote Originally Posted by Vinod View Post
    Hi ebaines,
    But the answer provided in the book is 6 hrs 53 minutes 20 seconds. Is that wrong?
    let $t_1=5$ and $t_2=3$

    $4 t_1 + 5 t_2 = 4*5 + 5*3 = 35$

    $5 t_1 + 4 t_2 = 5*5 + 4*3 = 37$

    the total time spent walking is $t_1+t_2=8 hrs$

    The book is incorrect, or you have not transcribed the problem correctly.
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  10. #10
    MHF Contributor ebaines's Avatar
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    Re: Ambiguous Problem

    You would get the answer provided by the book if the problem was changed slightly. If the girl walks 30 Km to the party, instead of 35 Km, and you leave the rest of the problem the same you get a total time of 6 hours, 53 minutes, 20 seconds.
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  11. #11
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    Re: Ambiguous Problem

    Hi ebaines,
    Yes,you are correct.
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