The solution is (see part (a)):

x = 100 - z + w
y = 75 - z + w
z, w arbitrary (and non-negative),

where

x = the hourly traffic down Rush St..
y = the hourly traffic down Pledge Ave.
z = the hourly traffic down Fasttrack Ave.
w = the hourly traffic down Depledge Blvd.

To obtain a particular solution, choose arbitrary non-negative values for z and w. Since we are told that w must be 1,000, we are left to choose a value for z, so let us take z = 0, giving

x = 1,100, y = 1,075, z = 0, w = 1,000

as one possible solution. There are lots of other possible ones (and infintely many, in fact, since the number of vehicles passing per hour need not be an integer.)

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