Two athletes practice for a marathon by running back and forth on a 11-mile course. They start running simultaneously, one at a speed 2 miles faster than the other. How fast does each run if they meet 1 hr 6 minutes after starting? (The faster one is already returning at this point.) How far from the starting point do the runners meet?

Answers

Answer 1

Answer:

Faster runner speed: 11 mph

Slower runner speed: 9 mph

Distance from starting point: 9.9 miles

Step-by-step explanation:

Let the slower runner speed be: x

Faster runner speed: x+2

1 hour 6 minutes = 1.1 hours

Slower: 1.1(x) = 1.1x miles

Faster: 1.1(x+2) = 1.1x+2.2 miles

This means that the faster runner had gone 2.2 miles more than the slower runner.

1.1x + 2.2 > 11 miles (This is true as we know the faster runner is coming back from the 11 mile run)

1.1x > 11 - 2.2 miles

1.1x > 8.8 miles

x > 8.8 / 2.2 miles

x > 8 mph

1.1x < 11 miles (we know this is true as the slower runner has to have gone less than 11 miles as the faster runner met him on his way back)

x < 11 / 1.1 miles

x < 10 miles

8 < x < 10

Although x could be any number including decimal between 8 and 10, the obvious first answer would be 9. However we need to check if this answer is correct.

Slower runner distance to the end:

1.1(9) = 9.9 miles

11 - 9.9 = 1.1 miles

Faster runners distance from the end (when coming back)

1.1(9+2) = 1.1(11) = 12.1 miles

12.1 - 11 = 1.1 miles

The speeds 9 mph and 11 mph are now proven to be the right speeds. Using our equation before, we can figure out the distance from the starting point that they meet at. This is just how far the slower runner has gotten. So, 1.1(9) = 9.9 miles from the starting point

Answer 2

The runners meet at a distance of 8.8 miles from the starting point.

How to determine the time required for two runners to meet each other

According to statement, each runner must run back and forth on a 11-mile course. After supposing that each runner moves at constant speed, expressions for each runner are presented below:

Fast runner reaches the end

[tex](v+2)\cdot 1.1 = 11[/tex] (1)

Fast runner comes back from the end

[tex]x = \left(v+2\right)\cdot (1.1-t)-(v+2)\cdot t[/tex] (2)

Slow runner meets fast runner

[tex]x = v\cdot 1.1[/tex] (3)

Where:

[tex]v[/tex] - Speed of the slow runner, in miles per hour.[tex]t[/tex] - Comeback time of fast runner, in hours.[tex]x[/tex] - Point of the track where runners meet each other, in miles.

By (1), we obtain the speed of the slow runner:

[tex]v = \frac{11}{1.1}-2[/tex]

[tex]v = 8\,\frac{mi}{h}[/tex]

The position from the starting point is calculated by (3):

[tex]x = (8\,mi)\cdot \left(1.1\,h\right)[/tex]

[tex]x = 8.8\,mi[/tex]

The runners meet at a distance of 8.8 miles from the starting point. [tex]\blacksquare[/tex]

To learn more on linear functions, we kindly invite to check this verified question: https://brainly.com/question/17058347


Related Questions

What are the domain and range of the function f(x)=square root x-7 +9?

Answers

Answer:

Domain is all real numbers greater than or equal to 7. Range is all real numbers greater than or equal to 9.

Step-by-step explanation:

The domain is possible x-values while the range is possible y-values. This question look like

[tex] \sqrt{x - 7} + 9[/tex]

The domain of square root function cant have a the radical inside being a negative number because we can't take the sqr root of a negative number and graph it on a cartisean plane We can take the sqr root of 0 . So we set x-7=0. And which x=7 so the domain is all real numbers that are equal to or greater than 7. The range of a sqr root function can only yield any positive y-values. So we must find the lowest point of it. Since the lowest x value we can possible use is 7 we plug it in

[tex] \sqrt{7- 7} + 9[/tex]

which equals 9. So the range is all real numbers greater than or equal to 9.

Answer:

I think that the short answer will be C) on edge.

Step-by-step explanation:

Edge 2021.

-7x2+1 need help plz

Answers

Answer:

-7 × 2 + 1 =

-13

Step-by-step explanation: I hope it helps.

Need help with this.......

Answers

Answer:

The length of the hypotenuse = 14 square + 10 square

The length of the hypotenuse =14×14 + 10×10

=296ft

Which system of inequalities has no solution?

Answers

Answer:

i think c

Step-by-step explanation:

Hi can someone please help me with this?​

Answers

It’s 36,000, because the total income in one year is 120,000 and if you subtract the total income from the tax paid per year you get the answer.
Hope this helped

PLS HELP ME IM STUCK ON THIS QUESTION

Answers

Answer:

ASA

Step-by-step explanation:

It is SAS (Side angle Side) because the lines on 2 of the triangle’s sides prove that they are congruent, and the 2 angles that are connecting the triangles are also the same.

PLEASE HELP ME ILL MAKE BRAINLIEST ​

Answers

Answer:

y=-3

Step-by-step explanation:

helpppp! The function f(x) = 4(2) models the
length of an image in centimeters after it
has been enlarged by 100% x times.
Which of these is the length of the image
after it has been enlarged 3 times?

Answers

Answer:

after it has been enlarged 3 times

Alfred has 10 more tokens than Clarissa. Clarissa has twice as many tokens as Benji. They have 85 tokens altogether. How many tokens does each person have.

Answers

Answer:

Alfred has 40 tokens

Clarissa has 30 tokens

Benji has 15 tokens

Step-by-step explanation:

Let's give each person a variable:

A for Alfred

C for Clarissa

B for Benji

Now, we can take what the question is saying and convert them into equations:

Alfred has 10 more tokens than Clarissa can look like this:

A = C + 10

Since Alfred has 10 more coins than Clarissa we can take C and add 10 to find how many tokens Alfred has.

Clarissa has twice as many tokens as Benji looks like this:

C = 2B

Since Clarissa has twice as many tokens as Benji we can multiply B (how many tokens Benji has) by 2.

Lastly, they have 85 tokens all together:

A + B + C = 85

We have these 3 equations:

A = C + 10

C = 2B

A + B + C = 85

Now, we can substitute some variables:

A = (2B) + 10    Since C is equal to 2B we can substitute 2B in for C in the first equation.

We have found what A equals, we can plug that in to the last equation:

(2B) + 10 + B + C = 85

We can also substitute the second equation into the third equation:

(2B) + 10 + B + 2B = 85

Combine like terms:

5B + 10 = 85

Solve

5B = 75

B = 15

This means that Benji has 15 tokens. Now we can find how much the other children have:

C = 2(15) = 30

Clarissa has 30 tokens

A = 30 + 10

A = 40

Alfred has 40 tokens.

Answer:

Alfred has 40 tokens

Clarissa has 30 tokens

Benji has 15 tokens

Checking the Answer

A + B + C = 85

40 + 15 + 30 = 85

85 = 85

I hope this helps!!

- Kay :)

To travel to school, Gavin must walk to the bus stop. The bus trip covers
four times the distance that he walks. He then needs to walk 500 m to
school. If the school is 10 km away from Gavin's home, how far does he
walk to the bus stop?

Answers

Answer:

2,375 m

Step-by-step explanation:

The computation of the distance from his walk to the bus stop is given below:

Let us assume he walks be x

So the bus trip be 4x

4x + 500m

From Home to school, it would be 10km

As we know

1km = 1000m

So for 10km it would be  = 10,000 m

4x + 500 m = 10,000 m

4x = 10,000 m - 500 m

4x = 9,500 m

x = 2,375 m

4 cm
5 cm
7 cm
10 cm
Work out the perimeter of this shape.

Answers

Answer:

34 centimeters

Step-by-step explanation:

Hope this helps! ;)

Answer: 34

Step-by-step explanation:

10+7+5+4+6+2= 34

Pls Help!! I'll Give BRANLISTT DUE SOOn

Answers

Answer:

whats the question? ill answer in comments

Step-by-step explanation:

I would love to help but you needed to put the image so we can help you :) .

Rosie has £m in her pocket she is given £4 pocket money write an expression for how much money she has now

Answers

Answer:

m+4

Step-by-step explanation:

She currently has a variable "m" in her pocket which we don't know, BUT we know how much she is getting, which is 4.

What are the factor pairs of 81.

Answers

Answer:

9 × -9 = 81, (-9, -9) is a pair factor of 81.

Step-by-step explanation:

All of the following fractions are equal to
2
except:
9
18
20
40
оооо
NEXT QUESTION
ASK FOR HELP

Answers

Answer:

Except 4 out of 6

the answer is the third one

The third one is not 1/2

It is important for engineers design and building so understanding the relationship between the height and volume of the building. A taller building if not billed correctly is more likely to collapse, because a small increase in height leads to a large increase in volume. an engineer builds to build a models of different sizes in the shape of square blocks . the smaller building has a height of 1m, and volume of 1m^3. The volume of the larger building is 125m^3. The height of the building, represented by X, is equal to the cube root of the buildings volume. The equation below can be used to find X, in meters. X^3=volume determine how much taller, in meters, the height of the larger building is then the smaller building.Mm

Answers

Answer:

Larger building is 4 meters taller than smaller building.

Step-by-step explanation:

Formula to get the height 'x' of a building having volume = x³ is,

x = [tex]\sqrt[3]{\text{Volume of the building}}[/tex]

Height of the smaller building,

[tex]x_1=\sqrt[3]{1}[/tex]

[tex]x_1=1[/tex]

Similarly, height of the larger building = [tex]\sqrt[3]{125}[/tex]

                                                               = [tex]\sqrt[3]{5^3}[/tex]

                                                               = 5 meters

Difference in the heights of the buildings = 5 - 1

                                                                     = 4 meters

Therefore, difference is the height of larger and smaller building is 4 meters.

Hope you are having a good day !!
I don't know if I can help much since i'm only in 7th grades as of Feb 2021, but if you are in my grade or lower I could probably help ! <3

Answers

Answer:

ok

Step-by-step explanation:

In a coffee shop, the average drink is currently $4.50 while the average pastry is $2.25. You've made a total of $5,250 today. Write an equation to model the breakdown of your sales between drinks and pastries.

Answers

Answer:

[tex]4.50x+2.25y=5,250[/tex]  where [tex]x[/tex] denotes number of drinks and [tex]y[/tex] denotes number of pastries.

Step-by-step explanation:

Let [tex]x[/tex] denotes number of drinks and [tex]y[/tex] denotes number of pastries.

Cost of the average drink = $4.50

Cost of the average pastry = $2.25

Total amount = $5,250

Therefore,

[tex]4.50x+2.25y=5,250[/tex]

(y - 3)-3/2+(y-3)-1/2=0

Answers

Answer:

y=4

Step-by-step explanation:

A ball is thrown straight up from the top of 128 foot building with an initial speed of 32 feet per second. How long will it take for the ball the hit the ground? How high will the ball be after 3 seconds?

Answers

The ball drops 32 ft per second
So.... 32 x 3 = 96 ft
So.... 128 ft - 96 ft = 32 ft in 3 sec
So .... 128 ft /32 ft = 4 seconds to hit the ground

Use Pascal's Triangle to help find the missing values. x^4-4x^b+6x^2-ax+1

a=

b=​

Answers

Answer:

The value of a = 4 , b = 3

Step-by-step explanation:

Given the equation,

x⁴ - 4[tex]x^{b}[/tex] + 6x² - ax + 1

so, the coefficients are -      1     4      6     a     1

the Pascal's triangle is as follows :

                                         1

                              1                     2

                   1                   2                        1

         1                   3                   3                         1

 1                4                   6                      4                       1

So,

from Pascal's triangle ,

we can see that , after comparing with given equation , we get

Row n = 4

The coefficient be 1 4 6 4 1

∴ we get

a = 4

and

(x+y)⁴ = x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴

Now, as given equation be x⁴ - 4[tex]x^{b}[/tex] + 6x² - ax + 1

By comparing we get y = -1 and b = 3

So, we get

a = 4 , b = 3

can someone pls pls find the value for (-14/9) x 3/5 x (-4/7) x 15/16​

Answers

(-14/9)x3/5x(-4/7)x15/16

=2/3x3/4
=1/2

5x – 2x = 12
How do I solve

Answers

Answer:

4

Step-by-step explanation:

Replace X with 4

(5*4)-(2*4) = 12

Answer:

x =4

Step-by-step explanation:

5x - 2x =12 (Subtract 5x - 2x and you'll get 3x)

3x = 12 (Now divide by 3 from both sides to get x)

x = 12/3 (Now that you got x, you want to simplify)

x = 4 (12 divided by 3 is 4)

The point Q(-6, 3) is reflected over the y-axis. What are the coordinates of the resulting
point, Q'?

Answers

Answer:

Q' = (6,3)

Step-by-step explanation:

You can think of this problem in two ways:

Graph:

I've shown my working for this, where I've counted how many units it takes to get from point Q to the axis through which im reflecting. There are 6 units between Q and the y axis, so naturally there should be 6 units between Q' and the y axis.

Coordinates:

Since this is a reflection through an axis, we can assume that the the x coordinate of point Q' will be equal and opposite to Q. Therefore, while the x coordinate of Q was -6, of Q' it's 6

Help please it finding the area of a composite figure

Answers

Answer: The answer is 468.

Explanation: the answer is 468 because 6 times 6 times 13 equals 468. So that’s the area of the composite figure.

How many triangles, if any, can be drawn with side lengths of 4 cm, 7 cm, and 15 cm?

Answers

Answer:

none

Step-by-step explanation:

the two shortest lengths combined have to be longer than the longest length

4+7=11

11<15

the 4 cm side and the 7 cm side wouldn't touch

It would be impossible beca if you add 4 and 7, you would get 11 as an answer and 11 is less than 15. In order to create a triangle, the first 2 measurements should be greater than the 3rd measurement or else the sides wouldn’t touch. Hopefully this helped you out !! C:

Please help me with this!

Answers

Answer:

-6

Step-by-step explanation:

Please help:

What are the solutions to the system of equations?

x^2 + y^2 = 5
y = 2x

The solution with the smaller x value is (?)
The solution with the larger x value is (?)

Answers

Answer:

(- 1, - 2 ) and (1, 2 )

Step-by-step explanation:

Given the 2 equations

x² + y² = 5 → (1)

y = 2x → (2)

Substitute y = 2x into (1)

x² + (2x)² = 5

x² + 4x² = 5

5x² = 5 ( divide both sides by 5 )

x² = 1 ( take the square root of both sides )

x = ± [tex]\sqrt{1}[/tex] = ± 1

Substitute these values into (2) for corresponding values of y

x = - 1 : y = 2(- 1) = - 2 ⇒ (- 1, - 2 )

x = 1 : y = 2(1) = 2 ⇒ (1, 2 )

The solution with smaller x- value is (- 1, - 2 )

The solution with the larger x value is (1, 2 )

Charlotte is at a baseball game in the upper deck of the stadium. She is 200
200
feet away from home plate. If the angle of depression to the field is 38°
38
°
, at what height above the field is Charlotte sitting?

Answers

Answer:

123.1323

Step-by-step explanation:

Graph:
Y=X +3 squared -4

Answers

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Other Questions
-2(x - 2) = -3 - 21 I need help with that question, I've been trying to solve it for hours but i cant find the answer According to Kennedys speech, what can space exploration teach people about safeguarding earths environment? 25 times 10*6 in normal form guys whats lumptatious mean? One of the most serious issues in the world today is inflation. Governments, private industry, and consumers share responsibility for the continued increases in the cost of living, but so far no solution that involves cooperation among these groups has been implemented Which is the meaning of the word "implemented" in the passage?improvedinventedput to usethrown away You should avoid having people in your photographs of signs. True False The Thirteenth Amendment made slavery illegal in the United States. Was it successful in making this happen? Why or why not? How many liters of solution would it take to make a 0.250 M solution when you have 3.52 moles of solute? A car park holds 480 cars when full. The probability of a car in the car park being silver is 0.375.On Friday morning the car park was full and Jamie counted 164 silver cars. Is this more or lessthan expected?Justify your answer by calculation Explain the difference between the common misconception people have about tax brackets and how they actually work My mother, along with all of my godparents, began planning my quinceaera after I turned fourteen. My mother and aunts took me tobridalshopwhere I was fitted for a long, white gown, which I would wear at the celebration. | felt my cheeks grow red with embarrassment as thewomen fawned and fussed over me in the store. I desperately wished that I couldust find a hole to crawl Into and hide, but there was no wayout. My mother, who was in her glory, naturally assumed that the redness In my faceIt was her day, I kept telling myself. was doing this for her.was glow of happiness. I let her go right on thinking that.At last, the big day came. My father cooked up a special breakfast for mybrothers and me first thing that morning. I had a queasy feeling In thepit of my stomach, but I was somewhat comforted by my father's easygoing manner and his apparent anticipation of the celebration ahead.After breakfast, my mother helped me dressfor the quinceaera. While she was styling my halr, she paused every soaffection for her. of Joy that had trickled down her face. I couldn't recall ever having seen my mother quite this happy, and suddenly my heart swelled with often to wipe avjay a tearTwo hours later, foundpews.myself standing In the front of a church while all of my dearest friends and family members gazed up at me fromafter all; it was for me. As I looked out on the smiling, supportive faces of all the people I loved, I had an unexpected realization. This daythewasn't for my motherThe church ceremony wasfollowed by a fiesta that lasted all day andInto the night. My Important to me. prepare. A disc jockey played all of the music I loved, and I was showered with beautiful gifts, practical advice, and parents served food that they had worked for days togood wishes from everyonestories about long-gone relatives. My heritage, I realized, was very real. As I watched my family members celebrate in my honor, I realized that my Mexican heritage was not something Intangible, like ; was with me at all times, and I was proud of it.bunch of oldWhat is the purpose of thisessay? 5.a. Are triangles ABC and DEF similar?Show or explain your reasoning. what is question for 6 For a group of objects made of the same material, the weight of an object varies directly with its volume. If an object has a volume of 20 cubic inches and weighs 28 ounces, what is the constant of variation? Based on the goal expressed by Steve Yancovich,which stage of the consumer decision-making processis eBay trying to influence? How are they doing so? Compare and contrast the Qin and Han Empiresbased on the maps. Select all correct answers. respuesta [tex]( + 2) ^{5} [/tex] If you are studying a gene within DNA and find out that guanine makes up 41% of it, how much is Adenine? For every dime spent DeVita receive 15 food Pepsi the animals in the petting zoo David has fed the animals a total of 135 food pebbles right in Savon equation to find the number of dimes Davida spent at the petting zoo Plz help me I really really need your help this is due today