Traffic Flow 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.
To find: The value of
Answer to Problem 60E
The value of
Explanation of Solution
Given:
Four variables
Four streets first, second, avocado, birch
Calculation:
Use the intersection logic,
The sum of cars entering and leaving each intersection must be zero.
For first and avocado street,
Simplify the above equation,
For first and birch street,
Simplify the above equation,
For second and birch street,
Simplify the above equation,
For second and avocado street,
Simplify the above equation,
By the simplifying equations the matrix is,
Apply
Apply
Apply
Apply
Apply
Apply
Apply
Last equation of the above matrix is
Linear equation of the above matrix,
For the solution let
The value of
The value of
The value of
The value of
Thus,
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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