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Math Help - Two linear equations problem.

  1. #1
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    Two linear equations problem.

    I have two problems that I'm having a hard time solving.

    Erin takes a total of 5 hours in her boat to travel a distance upriver and return downriver the same distance. If the time traveling upriver is twice the time traveling downriver, how many hours does each trip take?

    I need to get 2 equations out of it and use the matrix to solve the problem...
    The first equation I got from it is...
    U + D = 5 and the second is 2U = D...?

    The other problem I'm having trouble with is...

    Monica lives 16 mi. from her job. One morning she decides to get some exercise by jogging part of the way and taking the bus the rest of the way. She estimates she can average 4 mi/h jogging and 20 mi/h on the bus. If she allows 1 hour to get to work, how many minutes should she jog and how many should she ride? Write one equation for time and one for distance.

    I can't figure out the 2nd one at all.
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  2. #2
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    Quote Originally Posted by bnk0430 View Post
    I have two problems that I'm having a hard time solving.

    Erin takes a total of 5 hours in her boat to travel a distance upriver and return downriver the same distance. If the time traveling upriver is twice the time traveling downriver, how many hours does each trip take?

    I need to get 2 equations out of it and use the matrix to solve the problem...
    The first equation I got from it is...
    U + D = 5 and the second is 2U = D...? <<<<<<< that's correct. Since you have to use a matrix maybe this is better:
    U + D = 5
    2U - D = 0


    The other problem I'm having trouble with is...

    Monica lives 16 mi. from her job. One morning she decides to get some exercise by jogging part of the way and taking the bus the rest of the way. She estimates she can average 4 mi/h jogging and 20 mi/h on the bus. If she allows 1 hour to get to work, how many minutes should she jog and how many should she ride? Write one equation for time and one for distance.

    I can't figure out the 2nd one at all.
    There are 2 different distances: The jogging distance j and the bus riding distance b:

    j + b = 16

    According to the formula speed = \dfrac{distance}{time} the time for jogging is:
    t_j=\dfrac j{4\ \tfrac{mi}{h}}
    and the busriding time is
    t_b= \dfrac b{20\ \tfrac{mi}{h}}

    Both periods add up to 1 hour:

    \dfrac j{4\ \tfrac{mi}{h}}+\dfrac b{20\ \tfrac{mi}{h}} = 1\ h

    Can you take it from here?
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  3. #3
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    Thank you earboth, but for the 2nd question it is actually set up like this...

    J+B = 1
    4J+20B = 16

    I used the first question for time and 2nd question for distance instead of how you provided it. At first when I followed your steps the answer came out to be J = 1 and B = 12. After a couple of minutes of hard thinking and several times of rereading, I thought it would make more sense if the first equation would equal to time instead of distance and that's it! Without your guidance I would've never reach the conclusion on my own so thank you very much!

    Also I would have never thought of 2U-D = 0 on my own so again thank you.
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  4. #4
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    Quote Originally Posted by bnk0430 View Post
    I have two problems that I'm having a hard time solving.

    Erin takes a total of 5 hours in her boat to travel a distance upriver and return downriver the same distance. If the time traveling upriver is twice the time traveling downriver, how many hours does each trip take?

    I need to get 2 equations out of it and use the matrix to solve the problem...
    The first equation I got from it is...
    U + D = 5 and the second is 2U = D...?
    I can't imagine why you would use matrices to solve this- if D= 2U then the first equation becomes U+ 2U= 3U= 5.

    The other problem I'm having trouble with is...

    Monica lives 16 mi. from her job. One morning she decides to get some exercise by jogging part of the way and taking the bus the rest of the way. She estimates she can average 4 mi/h jogging and 20 mi/h on the bus. If she allows 1 hour to get to work, how many minutes should she jog and how many should she ride? Write one equation for time and one for distance.

    I can't figure out the 2nd one at all.
    If J+B = 1 then 4J+ 4B= 4.

    subtract that from 4J+20B = 16.
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