When two pipes fill a pool together, they can finish in 4 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours. How long will it take each pipe to fill the pool if it were working alone?

One pipe takes __ hours alone.
The other pipe takes __ hours alone.

Answers

Answer 1

One pipe takes 6 hours working alone.

The other pipe takes 12 hours working alone.

This is a rate of work problem. The formula utilized is

[tex]w=r\times t[/tex]

where

[tex]w[/tex] is the work done[tex]r[/tex] is the rate of work done[tex]t[/tex] is the time taken to do the work

We are looking for how long it will take each pipe to completely fill the pool

For pipe 1 working alone to fill 1 pool, the work done is 1;

[tex]w=r\times t\\\\1 = r_1 \times t_1\\\\t_1=\frac{1}{r_1}[/tex]

For pipe 2 working alone to fill 1 pool, the work done is 1;

[tex]w=r\times t\\\\1 = r_2 \times t_2\\\\t_2=\frac{1}{r_2}[/tex]

From the question, it would take 9 hours if each pipe took turns to fill half the pool. That is;

[tex]\frac{t_1}{2}+\frac{t_2}{2}=9\\\\t_1+t_2=18[/tex]

However, if both pipes worked together, it would take 4 hours for each pipe. That is;

[tex]w_1+w_2=w\\\\r_1t_1+r_2t_2=w\\\\4r_1+4r_2=1\\\\r_1+r_2=\frac{1}{4}[/tex]

Remember that [tex]r_1=\frac{1}{t_1}[/tex] and [tex]r_2=\frac{1}{t_2}[/tex]. So,

[tex]\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{4}\\\\\frac{t_1+t_2}{t_1t_2}=\frac{1}{4}[/tex]

Also recall that [tex]t_1+t_2=18[/tex]. So,

[tex]\frac{18}{t_1t_2}=\frac{1}{4}\\\\t_1t_2=72[/tex]

The only factors of 72 that satisfy the conditions

[tex]t_1+t_2=18\\\\t_1t_2=72[/tex]

are 6 and 12.

Therefore, pipe 1 will take 6 hours, and pipe 2 will take 12 hours to fill the pool if working alone.

The link below has a similar problem on rate of work

https://brainly.com/question/21485928


Related Questions

helppppppppppp i hv 5 mins

Answers

Answer: 342.5 miles

Step-by-step explanation:

Distance = Speed x Time

Speed(mph) Time(hr)   Distance(miles)

     55        x        3.5        =     192.5

     60         x       2.4        =     150

Total Distance (miles) =        342.5 miles

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!10

Answers

[tex]\huge \bf༆ Answer ༄[/tex]

The slope of the marked line is " Negative "

Lines that make obtuse Angle with positive x - axis have a Negative slope.

[tex]꧁  \:  \large \frak{Eternal \:  Being } \: ꧂[/tex]

Math 8 Question! :)

Four different positive integers have a mean (average) of 100. If the positive difference between the smallest and largest of these integers is as large as possible, determine the average of the other two integers.

Answers

Answer:

2.5

Step-by-step explanation:

"Four different positive integers have a mean (average) of 100"

The total of the 4 numbers is then 4* 100 = 400

"the positive difference between the smallest and largest of these integers is as large as possible"

to get the greatest difference the first 3 numbers must be

1, 2 and 3 which totals 6

the 4th number is then 400 - 6 = 394

the four numbers are 1, 2, 3 and 394

The greatest difference is between 1 and 394

"the average of the other two integers"

(2 + 3)/2 = 2.5

The average of the other two integers is 1.5.

What is the average of the two numbers?

An integer is an whole number. An example of an integer is 20.

If the mean of the four integers is 100. It means that the sum of the integers must be 400. If the integers are 0,1,2, 397. The largest number is 397 and the smallest number is 0. The average of the other two integers is (1 + 2 ) / 2 = 1.5

To learn more about mean, please check: https://brainly.com/question/25842202

If f(x) =x+1\x-1 and f(a) = 5 then f(2a) is equal to?

Answers

(2a) = 5*2 = 10
f(2a)= 10+1/10-1
=11/9

Draw a square and its diagonals. Guess the measures of these angles.

Answers

Answer:

90 degrees on each angle.

Step-by-step explanation:

A square is symmetrical on all sides, so each side has to be a right angle. Each right angle adds up to 360 degrees, the total degrees of a quadrilateral.

im so confused can someone help me please

Answers

Answer:

1. false

2. false

3. false

4. true

Step-by-step explanation:

a quadritilateral always has 4 sides, but it dpesnt HAVE to be a square

a parrellelogram can be any shap as long as its parrelel

a rhombus is always a square, becuase if you turn it around... VIOLA! you get a square.

Celeste wants to have her hair cut and permed and also go to lunch. She knows she will need $68. The perm costs twice as much as her haircut and she needs $5 for lunch .

Answers

Let P=Perm cost
Let H = Haircut cost
Let L = Lunch cost

Perm costs twice as much as haircut so.. P = 2H
L = 5

H + P + L = 68 the total cost is $68

H + 2H + 5 = 68 since P = 2H and L=5

3H + 5 = 68

3H =63

H = 63/3

H = 21

A Haircut is $21
Perm = 2H = 2(21) = $42

Answer:

42 dollars

Step-by-step explanation:

2h+h+5=68

3h+5=68

3h=63 divided by 3

21*2=$42

7 less than 6 times a number is equal to 9 more than 4 times a number. What is the number?

Answers

Answer:

Write an equation the represents the words.

6x - 7 = 4x + 9

To solve for x (the number), isolate it from the other variables.

Subtract 9 from both sides.

6x - 7 - 9 = 4x

Combine like terms.

6x - 16 = 4x

Subtract 6x from both sides.

-16 = 4x - 6x

Combine like terms.

-16 = -2x

Divide both sides by -2.

-16/-2 = x

x = 8

The number is 8.

Hope this helps! :)

Answer:

The number is 8.

Step-by-step explanation:

Hello there!

We're given an unknown number, let's call this number n

We know that 7 less than 6 times n is equal to 9 more than 4 times n

Let's break that statement down, starting with "7 less than 6 times n"

6 times n should be 6n, since 6 * n = 6n

"7 less" means subtraction.

So "7 less than 6n" should be 6n-7

Now with "9 more than 4 times n"

4 times n should be 4n, as 4 * n = 4n

"9 more" means addition

So "9 more than 4n" should be 4n+9

The statement says that 6n-7 is equal to 4n + 9, and so when we write it as an equation:

6n - 7 = 4n + 9

Now we can solve the equation

Subtract 4n from both sides

2n - 7 = 9

Add 7 to both sides

2n = 16

Divide both sides by n

n=8

The number is 8

PS. we can substitute 8 back into the equation as n to see if it works:

6(8)-7=4(8)+9

Multiply

48-7=32+9

41= 32 + 9

41=41

It works :))

Hope this helps!

PLZ HELP!!!!!!!!!!!!!!​

Answers

Answer:

183in^2

Step-by-step explanation:

Given that the length is 15 in and the width is 26 in we can figure out the area of a full rectangle.

15x26=390in

We now want to figure out the small rectangle on the bottom of the image.

The area of a triangle is A=hb/2

A=6x15/2=45

In the image, you can see that the rectangle is incomplete and missing part of it. It's missing a triangle so in order to complete the rectangle you multiply 45x2.

45x2=90

Finally, we can solve for the remaining triangle.

A=9x26/2=117

Add up the triangles and subtract the sum from the area of the rectangle to get the shaded area.

390-(90+117)=183in^2

Hope this helps :)

457x64-(163+208x45) + ( 2820÷20)-1802

Answers

Answer:

18064

Step-by-step explanation:

these equations are always in this order:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

To remember this, my teacher told us the phrase; "Please Excuse My Dear Aunt Sally".

y=6x-4 y=4x+2 substitution pls help plsplslsl​

Answers

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:  ( 3 , 14 )

Equation Form:  x  =  3 , y  =  14

Step-by-step explanation:

The weights of 2-pound bags of Best Dog Food are approximately normally distributed with a given mean Mu and standard deviation Sigma. According to the Empirical Rule, what percentage of the bags will have weights within 3 standard deviations of the mean? 47. 5% 68% 95% 99. 7%.

Answers

I think it’s 68 percent

A chartered vacation will cost eva $1,250 plus $45 per day for food. If Eva wants to spend less than $1,700, how many days can she travel?

Answers

Answer:

She can travel for 10 days

Step-by-step explanation:

first you do 1,250 divided by 1,250 will equal 0. Then you do the other side 1,700- 1,250 =450. Then you do 450 divided by 45 and you will get 10

Hope this helps you out!

If I add 60 to 325 and then subtract 40, the answer I get will be equal to

Answers

Answer:

345

Step-by-step explanation:

On adding 60 to 325 and then subtracting 40 the answer will be 345.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given numbers 60, 325, and 40. The expression will be formed as below:-

E = 60 + 325 - 40
E = 385 - 40

E = 345

Therefore, on adding 60 to 325 and then subtracting 40 the answer will be 345.

To know more about an expression follow

https://brainly.com/question/28177534

#SPJ2

Quadrilateral ABCD has the following
vertices:
A(2, 7)
B(8,1)
C(1, -9)
D(-6, -2)
Is quadrilateral ABCD a parallelogram, and
why?

Answers

Answer:

No because the angle of point C is NOT congruent to the angle of point A.

Step-by-step explanation:

A quadrilateral MUST be a parallelogram if it has both pairs of its opposite angles congruent.

Help please important if you help you get brain lay

Answers

[1] 1/2

    - It will be 1/2 as large because of the scale factor

[2] 1/4

    - 1/2 * 1/2 = 1/4

[3] (1/2)n

    - For every scale factor (n), there will be a chance of 1/2

Have a nice day!

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Astore pays $927.40 for a water heater and marks the price up by 5%. What is the new price?

Answers

Answer:

$973.77

Step-by-step explanation:

$927.40 = 100%

New price = 100% + 5%

New price = 105% of 927.40

105% of 927.40 = 1.05(927.40)

1.05(927.40) = 973.77

-Chetan K

[tex]\sqrt{x}(-5-(-8))x^{2} +(-5-(-7))x^{2}[/tex]

Answers

[tex]\sqrt{x} (-5-(-8))x^{2} +(-5-(-7))x^{2} = 3.x^{2} \sqrt{x} +2x^{2} = x^{2} (3\sqrt{x} +1)[/tex]

ok done. Thank to me :>

Brian invests £7500 into his bank account.
He receives 6% per year compound interest.
How many years will it take for Brian to have more than £10000?

Answers

Answer:

5 years

Step-by-step explanation:

What is the value of x in the triangle?

Answers

[tex]cosec18°= \frac{perpendicular}{base} \\ cosec18°= \frac{25}{x} \\ \\ \ \: since: cosec18°=0.9511 \\ \\ 0.9511 = \frac{25}{x} \\ x = \frac{25}{0.9} = 26[/tex]

Julie has a square-shaped driveway with an area of 256 square feet. What are the dimensions of the driveway?

A. 64ft x 4ft

B . 15ft x 15ft

C. 16ft x 16ft

D. 32ft x 8ft

Answers

Answer:

16ft x 16ft

Step-by-step explanation:

Square shaped, so side lengths are all the same size, so 16ft by 16ft. 256 would also need to end in a 5 to be a product of 15 by 15 but would end in six for 16x16 (5*5 and 6*6 will show last digit of the number)

What are the roots of the equation?
5x^3 + 45x^2+ 70x = 0

A) -2, 0, 7
B) -7, -3, 0
C) -7, 0 , 2
D) 0, 2, 7

Answers

Answer:

D) 0, 2, 7

Step-by-step explanation:

Hope this helps

the ratio of men to women at Wal-Mart was 3 to 5. If there were 350 women, How many men were in the store?

Answers

Answer:550

Step-by-step explanation:

Answer:

550

sjjeusuwjwhhsusjsisjisjwnqbisjd

help me with this one guys......

Answers

Answer:

[tex]7^-^1[/tex]

Step-by-step explanation:

So, when multiplying numbers with exponents that have the same base, all you have to do is combine the exponents.

what is (−
2
1

)
5

Answers

Step-by-step explanation:

i don't understand your question

That isn’t even a question! Sorry. But if it was i could answer it

1 point
10.) Tampa is about 275 miles from Tallahassee. How far about would they
be on a map with a scale of 1 in. = 15 mi?
20 inches
20.25 inches
O
19.24 inches
18.33 inches

Answers

Answer:

18.33

Step-by-step explanation:

its easy divide 275 ÷ 15 = [18.33]333333333333 the only number you need is [18.33]333333333333

and boom that simple you get your answer

How do i find the slope-intercept form for 6x=8y+10

Answers

Answer:

y = 3/4x - 5/4

Step-by-step explanation:

6x=8y+10

Well you must first get your equation set up into the form called "Slope intercept."

6x=8y+10

Add 8y on both of your sides because your y is suppose to be alone.

8y + 6x = 10

Subtract 6x on both sides since it is in fact the opposite of addition.

8y = 6x + 10

Now, you will divide by 8 on both sides. When doing this your y will be alone.

y= 6/8x + 10/8

Note: You can leave it like this but you want to probably simplify.

y = 3/4x + 5/2

      or

y = 3/4x - 5/4

(Hope this helps can I pls have brainlist (crown)☺️)

If you subtract ¾ by ¼,what is the difference?

Answers

[tex] \frac{3}{4} - \frac{1}{4} \\ = \frac{3 - 1}{4} \\ = \frac{2}{4} \\ = \frac{1}{2} [/tex]

- BRAINLIEST answerer

2/4 is the difference

20 + 3xy - 4xy +y2 + 10 -y2

Answers

Answer:

−xy−y2+2y+30 is the answer simplified

A pool with a square bottom is to have a volume of 2000 cubic feet. The owners plan to use a fancy tile to complete the pool. The sides of the pool will cost $80 per square foot and the bottom of the pool will cost $40 per square foot. Find the pool dimensions that will minimize the cost of construction.

Answers

Considering the given conditions in the question, the dimensions that will minimize the cost of construction of the pool are:

base length = 10 feet

base width = 10 feet

pool depth = 20 feet

Volume of a material implies the maximum amount of substance that it can contain.

From the given question, it is expected that the pool would have the shape of a cuboid, thus its volume can be determined by:

volume of the pool = length x width x height

                                = base area x height

Thus, given that the volume of the pool is 2000 cubic feet, then;

2000 = base area x height

i. Let the dimensions of the square base be 10 feet, and its height 20 feet, so that;

volume = 10 x 10 x 20

            = 2000 cubic feet

The cost of constructing the pool of the assumed dimensions would be:

Total area of its sides = 4 x 200

                                    = 800 square feet

The cost of tiling the sides of the pool = $80 x 800

                                         = $ 6400.0

Area of the base of the pool = 10 x 10

                                            = 100 square feet

The cost of tiling the base of the pool = $40 x 100

                                         = $4000

Total cost = $6400 + $4000

                 = $10400

Total cost of constructing the pool with the assumed dimensions is $10400.

ii. Let the dimensions of the square base be 20 feet, and its height 5 feet, so that;

volume = 20 x 20 x 5

            = 2000 cubic feet

The cost of constructing the pool of the assumed dimensions would be:

Total area of its sides = 4 x 100

                                    = 400 square feet

The cost of tiling the sides of the pool = $80 x 400

                                         = $ 32000

Area of the base of the pool = 20 x 20

                                            = 400 square feet

The cost of tiling the base of the pool = $40 x 400

                                         = $16000

Total cost = $16000 + $32000

                 = $48000

Total cost of constructing the pool with the assumed dimensions is $48000.

Therefore, the dimensions that will minimize the cost of construction of the pool are:

base length = 10 feet

base width = 10 feet

pool depth = 20 feet

Visit: https://brainly.com/question/16955358

Other Questions
Nowadays, many of the huge factories and industries ___________to function if there was no adequate electric power. Can someone help me with this? I was wrong and cant figure it out Which of the followingis true according to the5th Amendment?A. People who are accused of crimes do not have togive testimony against themselves.B. People who are accused of crimes must givetestimony against themselves if necessary.C. People who are accused of crimes do not have theright to hear any witnesses against them. Find the slope of the line that passes through:(6,7) and (4,2) Answer my question please!! I will give u 40 points!!!Does the term Dark Ages apply to the Middle Ages in the Islamic World? Explain your answer. at 6 am the temperature was -8C. In the afternoon, the temperature was +3C. What was the change of temperature during the day? Exercise BWrite whether the items below are independent or dependent clauses. If aclause is dependent, rewrite it and add an independent clause to make acomplete sentence. If a clause is independent, rewrite it with the correctcapitalization and punctuation.Example: since I was boredAnswer: dependent-Since I was bored, I went to a movie. or I went to amovie since I was bored.1. a show always entertains2. because a friend recommended it3. though the show was great4. I kept quiet5. if it was a sad scene What is -3/10 + 3/10 = what rule is this, please answer correctly, please answerrrrrrrrrrrr plssssssssssssssssssssssssssssssss what is the trend of the graph of the equation y = 3x + 10 Choose the correct vocabulary word from each drop-down menu to complete the sentences.(A) The detective had a 1. migrate 2. theory 3. Energetic about who committed the crime.(B ) The birds will1. Flurry2. theory 3. migratewhen the seasons change.( C ) I was tired earlier, but now I'm feeling more1. Disappearance 2. Energetic3. FlurryThe choices are the 1-3 please pick a number from every letter (A-C) what is the importance of the floriculture in nepal please what is the answer fast very Complete the expression that represents the prime factorization of 492.Type the factors in the increasing order.492 = 2 2 A nurse is teaching a client who is 30 weeks' pregnant about ways to deal with pyrosis (heartburn). The nurse determines a need for additional teaching based on which client statement Which Chief Justice wrote the majority opinions in over 500 cases, including McCulloch v. Maryland and Gibbons v. Ogden?John MarshallRoger TaneyJohn JayOliver Ellsworth what is frost shattering Which law gives an organization more instruction and insight into the type of information security plans/policies required Which of the following statements are correct?Please help