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Math Help - Matrices Word Problem

  1. #1
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    Dec 2007
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    2

    Matrices Word Problem

    Hello all!

    I'm am trying to wrap up the last of some homework applying algebra to matrices. I'm stuck on a word problem I just can't seem to figure out how to begin. If anyone could point me in the right direction, I would appreciate it. Here's the situation:

    A section of a city's street network is shown in the figure. The arrows indicate one-way streets, and the numbers show how many cars enter or leave this section of the city via the indicated street in a certain one-hour period. The variables x, y, z and w represent the number of cars that travel along the portions of First, Second, Avocado, and Birch Streets during this period. Find x, y, z and w, assuming that none of the cars stop or park on any of the streets shown.

    I'm then given a simple illustration. The first horizontal street is First, traffic moving from left/west (200 cars enter) to right/east (20 cars exit). The second horizontal street is Second, moving right (200 cars enter) to left (400 exit). The western vertical street is Avocado, travels top/north (180 enter) to bottom/south (200 exit). Birch, the eastern and final road, also travels top (70 enter) to bottom (30 exit). The best diagram I can render with characters:

    Code:
     (Avocado St)          (Birch St)
    
             180             70
               |               |
               |               |
       200 --> V       x       V --> 20      (First St)
    
               z               w
    
       400 <-- |       y       | <-- 200     (Second St)
               |               |
               V               V
              200             30
    I'm not entirely sure what structure I should use to solve this. I've tried a lot of strange addition, subtraction and complete hooey matrices that don't solve for anything that makes sense. Five pages of sad math later, I'm here for help. This assignment is due tomorrow morning, but I'd like to know how to work it out regardless as we'll be testing on the subject Friday.

    Please and thanks in advance!
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  2. #2
    Newbie
    Joined
    Dec 2007
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    5

    re matricices word problem

    from Birch st (70 cars) drive down until (20 cars) turn left into and exit First st.
    (50 cars) continue until they get to Second st. (30 cars) continue on down exiting Birch st.
    which leaves us (20 cars) from Birch st. these are joined by the (200 cars) entering Second st, so now (220 cars) cross over and exit Second st. From Advocado st (180 cars) travel down and turn right into second st. join the two lots together 220+180 gives you your 400 exiting Second st. Bring your (200 cars) out of First st. turn right and continue on until you exited Birch st .

    Now you have your entrances (well you always did) and your exits hopefully this will help you to work out how many cars pass your W,X,Y and Z at certain points to give you your totals.
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  3. #3
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    Joined
    Dec 2007
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    Thank you for the reply.

    I see what you're saying, and that does end up with a specific number of cars passing each section of variable. But it seems like there would be more than one answer. While 70 cars may leave from the north side of Birch street, there's a chance that only 10 turn off or none, and the remaining cars that exit on First could come from the cars that started out entering the system on First to begin with.

    Since it's matrices, this sounds a lot like I should be able to break this info up into equations, derive matrices from them and then find that there are infinite solutions as described in terms of one variable. Am I over-thinking this or do I just not see some math you're doing?
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