Mathematics Middle School

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?

Answers

Answer 1

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 4.5 miles

Answer 2

The length of the Green Route in miles is 4.5 miles.

Formulate an equation for Monday and Tuesday

Monday

6x + 5y= 52............Equation 1

Tuesday

12x + 13y = 119............Equation 2

Multiply the equation  

12x + 10y= 104

-3y=-15

Divide both side by 3y

y=15/3

y=5

Plug in 5 into equation 2

12x + 13 (5) = 119

12x+65=119

12x=119-65

12x= 54

Divide both side by 12x

x=54/12

x= 4.5 miles

Inconclusion the length of the Green Route in miles is 4.5 miles.

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