what is the length of the green route in miles?

The correct answer is G) 4.5 mi.

Let b be the length of the blue route and g be the length of the green route:

6g+5b=52
12g+13b=119

We will use elimination to solve this.  We will make the coefficients of g equal by multiplying the first equation by 2:
2(6g+5b=52) → 12g+10b=104

Now we will subtract the second equation from this:
  12g+10b=104
-(12g+13b=119)
-3b=-15

Divide both sides by -3, and we have
b = 5

Substitute this into the first equation:
6g+5(5)=52
6g+25=52

Subtract 25 from both sides:
6g=27

Divide both sides by 6:
g = 27/6 = 4.5