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:
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.
(Avocado St) (Birch St)
200 --> V x V --> 20 (First St)
400 <-- | y | <-- 200 (Second St)
Please and thanks in advance!