A bus travels two different routes: the Green Route and the Blue Route, which vary in length.- On Monday, the bus traveled the Green Route 6 times and the Blue Route 5 times, covering a total of 52 miles.- On Tuesday, the bus traveled the Green Route 12 times and the Blue Route 13 times, covering a total of 119 miles.What is the length of the Green Route in miles? A) 4.4 mi B) 4.5 mi C) 6.4 mi D) 6.8 mi

To find the length of the Green Route, we can set up a system of equations based on the information given.

Let G represent the length of the Green Route in miles and B represent the length of the Blue Route in miles.

On Monday, the bus traveled the Green Route 6 times and the Blue Route 5 times, covering a total of 52 miles. This can be represented by the equation: 6G + 5B = 52 (Equation 1)

On Tuesday, the bus traveled the Green Route 12 times and the Blue Route 13 times, covering a total of 119 miles. This can be represented by the equation: 12G + 13B = 119 (Equation 2)

Now we can solve the system using the method of substitution or elimination. Let's use the elimination method to solve these equations:

First, we can double Equation 1 to help eliminate one of the variables: 2(6G + 5B) = 2(52) 12G + 10B = 104 (Equation 3)

Now we have a system with two equations, 3 and 2: 12G + 10B = 104 12G + 13B = 119

Subtract Equation 3 from Equation 2: (12G + 13B) - (12G + 10B) = 119 - 104 12G + 13B - 12G - 10B = 15 3B = 15

Divide both sides by 3 to find B: B = 15 / 3 B = 5

Now that we know the Blue Route is 5 miles, we can substitute this value back into either Equation 1 or Equation 2 to find G. Let's use Equation 1:

6G + 5B = 52 6G + 5(5) = 52 6G + 25 = 52

Subtract 25 from both sides: 6G = 52 - 25 6G = 27

Divide both sides by 6 to find G: G = 27 / 6 G = 4.5

Thus, the length of the Green Route is 4.5 miles, which corresponds to option B) 4.5 mi.