Abus travels two different routes the green route and the blue route the routes are different langths. 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.

The length of green route is 4.5 miles

Solution:

Let the length of green route be "x" miles

Let the length of blue route be "y" miles

On monday the bus traveled the green route 6 times and the blue route 5 times traveling a total of 52 miles

Therefore, we can frame a equation as:

6x + 5y = 52 ------- eqn 1

On Tuesday the bus traveled the green route 12 times and the blue route 13 times traveling a total of 119 miles

Therefore, we can frame a equation as:

12x + 13y = 119 -------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

12x + 10y = 104 -------- eqn 3

Subtract eqn 2 from eqn 3

12x + 10y = 104

12x + 13y = 119

( - ) --------------------

-3y = -15

3y = 15

y = 5

Substitute y = 5 in eqn 1

6x + 5(5) = 52

6x + 25 = 52

6x = 52 - 25

6x = 27

x = 4.5

Thus length of green route is 4.5 miles