A bus travels two different routes: the Green Route and the Blue Route. The routes are different lengths.
On Monday the bus traveled the Green Route 6 times and the Blue Route 5 times, traveling a total of 52 miles.
On Tuesday the bus traveled the Green Route 12 times and the Blue Route 13 times, traveling a total of 119 miles.
What is the length of the Green Route in miles?
Let's denote the length of the Green Route as "G" and the length of the Blue Route as "B."
From the information given, we can create a system of equations:
6G + 5B = 52
12G + 13B = 119
Now, we can solve this system of equations to find the length of the Green Route:
Multiply the first equation by 2:
12G + 10B = 104
Subtract the first equation from the second equation:
3B = 15
B = 5
Now we can substitute the value of B back into the first equation to find the length of the Green Route:
6G + 5(5) = 52
6G + 25 = 52
6G = 27
G = 27/6
G = 4.5
Therefore, the length of the Green Route is 4.5 miles.