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.

We are given w = 50, so the first two equations in the solution become

x = 150 - z
y = 125 - z.

The first equation asserts (among other things) that z cannot exceed 150 (or else x would be negative).
The second equation asserts (among yet other things) that z cannot exceed 125 (or else y would be negative).

Since all the equatoins must hold simultaneaously, it follows that z cannot exceed 125. Thus, at most 125 vehicles per hour drive down Fasttack Ave.

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