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.

Learn more about length here:https://brainly.com/question/24259483

Related Questions

A map has a scale of 3 cm : 18 km. If Riverside and Smithville are 54 km apart then they are how far apart on the map?
rainliest plz solve

Answers

Riverside and Smithville will be 9 km apart on the map. For every 6 km they will be 1 cm apart on the map.

54 km is 3 times of 18km and 3 times of 3 cm is 9 cm. So, Riverside and Smithville are 9 cm apart on the map.

Ratio and proportion:

Important information:

The given scaling ratio is 3 cm : 18 km.Riverside and Smithville are 54 km apart.

We need to find the distance between Riverside and Smithville in the map.

Let x cm be the distance between Riverside and Smithville in the map. The distance in the map and the actual distance are always proportional.

[tex]\dfrac{x}{54}=\dfrac{3}{18}[/tex]

[tex]x=\dfrac{3}{18}\times 54[/tex]

[tex]x=9[/tex]

Therefore, Riverside and Smithville are 9 cm apart on the map.

Find out more about 'Ratio and proportion' here:

https://brainly.com/question/11892195

The formula for calculating power is work divided by time (power = work ÷ time). What are two ways of stating the same relationship?

Answers

Answer:

1. work= time x power

2. work ÷ power = time

Step-by-step explanation:

hope this helps :)

Answer:

work=time x power

work divided by power =time

Step-by-step explanation:

Bobby runs a lemonade stand to raise money for Baker Children's Hospital. Last weekend, he made 8 quarts of lemonade to sell. Saturday was rainy, so he only sold 6 cups. The weather was better on Sunday, so he sold 18 cups. How many quarts of lemonade does he have left?

Answers

Answer:

2 quarts left

Step-by-step explanation:

8 quarts is 32 cups
32-24= 8
8 cups is 2 quarts

find the surface area, please

Answers

Answer:

52 cm^2

Step-by-step explanation:

6+12+8+26

26x2=52

Answer:24 or 32

i hope this helps and stay safe!!!!! <3

give me a real answer or else

Answers

Answer:

1. scholars team is 15 %, student gov. 0.08%, band 24%,  sports 34 %, fun raising is 17%

2. athletics is 30%, gov is 0.07 %, band is 21%, fund raising is 15%, scholars team is 14%

Step-by-step explanation:

Help....please I don’t want to fail.

Answers

the answer to this is 6
Here’s an explanation.

Cross multiply.
2 *21
7* x

42 = 7x
Divide each side by 7

x = 6

I need help On this ASAP

Answers

1. On week three is when she had a negative
Week 3 she had a negative.

Helpp mee pleaseeeeeeeeee and no messing around i need the answer

Answers

Answer:

I think it is 12 cm...

:D

Surface area equals 52
This is because length is 4cm width is 2cm and height is 3cm do just use the formula for a rectangular prisms surface area which is A=2(w l + h l + h w)

Karris ran eight eighteenths of a kilometer and cycled nine eighteenths kilometers in a race. How many kilometers was the race in all?

1 kilometer
seventeen thirty sixths kilometer
one eighteenths kilometer
seventeen eighteenths kilometer

Answers

seven eighteenths kilometer
The last one 17 18th kilo

help me again. i need help. thx 4 helping

Answers

Answer:

16 square units

Step-by-step explanation:

The formula for the area of a right triangle is ab/2 (a and b both being legs).

First, we find the legs' length which is MK and JK.

Since both points J and K are on the same y level, we look at the X coordinates and see how far apart they are.

Since both points M and K are on the same x level, we look at the Y coordinate.

M is 4 points away from K, so the leg MK is 4 units long.

J is 8 points away from K, so the leg JK is 8 units long.

Plug this into the formula and we get

[tex]\frac{4*8}{2}[/tex]

[tex]\frac{32}{2} = 16[/tex]

What is the circumference of the FIRST triangle nd how did you do it bc I WANT TO DO THE REST THX

Answers

Answer:

4... and I looked it up so i dont know

how many pieces of string, each 1/5 m long, can be cut from a string 3 m long?

Answers

Answer:

15 pieces

Step-by-step explanation:

15 pieces of string.

Help Pleaeaeaeaeaeaeaeaeaeaeease

Answers

Answer:

x=5

Step-by-step explanation:

First distribute then go from there
Your answer should be X=5

Answer as much as you can will give brainliest if correct

Answers

8) B
Don’t know the rest sorry

Maya is driving 120 miles to her grandmother’s house. She drives 35% of the distance before stopping for lunch. How far does she drive before lunch?

A. 78 miles
B. 36 miles
C. 85 miles
D. 42 miles

Answers

your answer is c. 85 miles your welcome

Which property is illustrated by the statement 8+2 = 2+8
a. associative
b. commutative
c. distributive
d. identity

Answers

Answer:

B. Commutative

Step-by-step explanation:

Commutative means to swap or moved from their positions.Hope this helps

B:commutative

It means to switch there places from there original spots hope this helps

Ten bagels and four muffins cost $13. Five bagels and eight muffins cost $14. How much does a bagel cost? How much does a muffin cost? (do not put $ in your answer)

Bagel:
Muffin:

Answers

Answer:

b= .80     m= 1.25

Step-by-step explanation:

Bagels would cost .80 and muffins 1.25

who ever answers first I will put as brainliest :D

Answers

Answer:

15 pounds of meat

Step-by-step explanation:

Answer:

15 Pounds of Hamburger Meat

Step-by-step explanation:

The ratio is 5lb/$10

Since $30 is 3 times the $10 then you multiply the 5 by 3 and it comes out to 15lb of meat

Determine the measure of the unknown angle in each triangle​

Answers

Answer:

78 degrees

Step-by-step explanation:

If you look at it, 2 of the angels are the same- those angels are A and B- the angel we are looking for. Angel A is 78 degrees and if angel A and angel B are equal then angel B is also 78 degrees.

Please help me
(preferably the last person plz)

Answers

Answer: Its -5z+6 sorry if its wrong

Step-by-step explanation:

-1/4 x 4 (5x+6)

-(5x+6)

= -5x-6

The answer is -5x-6

Water flows through a hose and fills a 100-gallon tank in eight minutes. When represented as a rate, in gallons per minute, what is the unit rate?

800
0.08
18
12.5

Answers

Answer:

B. 12.5

Step-by-step explanation:

It’s 12.5 the last one

Find the percent of decrease from 12 home runs to 9 home runs. I need this FAST!

Answers

Answer:

75%

Step-by-step explanation:

there are 4 3s in 12 and 9 is 3 of those 3s so 75%

can someone help me out? :P (serious answers only.)

Answers

Answer:

The answer is C 841.62.

I actually got 842.11, but C is the closest answer so that's gonna be the one.

Step-by-step explanation:

explanation to top answer^^^^^ first fine the area of the triangle. you have the diameter, 35, so it should be easy to figure it out. all you have to do next is find the area of the triangle, and then subtract the area of the triangle from the area of the circle!

How many gifts would you receive if you received all of the gifts in the song The Twelve Days of Christmas?

In what Christmas movie and which character said, "We elves try to stick to the four main food groups: candy, candy canes, candy corn, and syrup?"

Answers

You would maybe receive 12 gifts like the name implies?

Answer:

You would get 78 gifts. I think. The movie is Elf

Step-by-step explanation:

If you add 12+11+10+9+8+7+6+5+4+3+2+1= 78. And the movie is ELF. Hope this helps let me know if correct!!

Need help please 15 points

Answers

Answer:

Paula's tub filled much more faster becasue it has less water to fill up

Step-by-step explanation:

Evaluate the expression 2(5x -3y) if x = -1/2 and y = 1

Answers

the answer is -11!
once plugged in, the new equation would be 2(-2.5 -3)
this would equal 2(-5.5)
the final answer would be -11

I'd like an explanation on how to factor and simplify 1 - 2sin²x + sin⁴x and turn that into cos⁴x

thank you!

Answers

Answer:

I unveil the mysteries and secrets of trigonometry & you'll love it.

Step-by-step explanation:

PLZ HELP!!
MATCHING: Compare the fractions from Column B to the given percent's in Column A. Match the fractions that are the closest values of the given percent's. Not all fractions will be used.
Column A
1. ___ 41%
2. ___ 23%
3. ___ 98%
4. ___ 67%
5. ___ 34%
6. ___ 12%
7. ___ 48%
8. ___ 76%
Column B
A. 3/10
B. 1/2
C. 1/4
D. 5/5
E. 2/3
F. 1/3
G. 1/10
H. 3/4
I. 9/10
J. 4/5
K. 2/5

Answers

1. K

2. C

3. D

4. E

5. F

6. G

7. B

8. H

The table shows the relationship between the number of drops of food color added to different number of cups of cake frosting:


Cups of | Drops of
Frosting | Food Coloring
2 | 4
3 | 6
4 | 8


Which point below shows an equivalent ratio in this situation?

A. Point T, because if drops of food coloring are 50, then cups of frosting will be 100

B. Point G, because if cups of frosting are 40, then drops of food coloring will be 20

C. Point T, because if cups of frosting are 50, then drops of food coloring will be 100

D. Point G, because if drops of food coloring are 40, then cups of frosting will be 20

I'm guessing it's possibly C...? Please help me, and thank you!

Answers

I believe the answer is b

PLS HELP DUE SOON: (basically it's a retest) will give brainliest <3

Answers

The answer is the fourth one
If I’m correct I believe it’s 4.
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