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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?
A) 4.4 mi
B) 4.5 mi
C) 6.4 mi
D) 6.8 mi

Respuesta :

Set up a system of equations and say green route is x and blue route is y

This will give you
Monday 6x + 5y= 52
Tuesday 12x + 13y = 119

Solve by multiplying the top equation by two to get
12x + 10y= 104

Since you have 12x in both equations, these cancel out when you subtract the bottom from the top. This leaves you with

-3y=-15
Y=5

The blue route is 5 miles, but they want to know the green route. Fill in the y value in either one of your equations. Let’s use the one from Tuesday

12x + 13 (5) = 119
12x= 54
X= 4.5

This means that the answer is B, 4.5 miles

The length of the Green route is 4.5m and the length of the Blue route is 5m and this can be determined by forming the linear equation.

Given :

  • 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.

Let the length of the Green route be 'a' and the length of the Blue route be 'b' then on Monday bus traveled:

[tex]6a +5b=52[/tex]   ---- (1)

On Tuesday the bus traveled:

[tex]12a + 13b = 119[/tex]  ----- (2)

Now, solve the equation (1) for 'a'.

[tex]a =\dfrac{52-5b}{6}[/tex]     ------ (3)

Now, put the value of 'a' in equation (2).

[tex]12\left(\dfrac{52-5b}{6}\right) + 13b = 119[/tex]

[tex]104-10b+13b=119[/tex]

[tex]104+3b=119[/tex]

b = 5 m

Now, put the value of b in equation (1).

[tex]12a +13\times 5 = 119[/tex]

a = 4.5 m

For more information, refer to the link given below:

https://brainly.com/question/21835898

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