Let us say that:
x = the time it take for the new pump to drain the pool alone
4x = the time it take for the older pump
And we are given that together they drain the pool in 4 hours, therefore:
1/x + 1/4x = ¼
Multiply everything by x:
1 + ¼ = ¼ x
1.25 = 0.25 x
x = 5 hours
So, 4x = 20 hours
Hence it take the older pump 20 hours draining alone.
Final answer:
The older pump would take 3.2 hours, or 3 hours and 12 minutes, to drain the pool on its own, since it takes 4 times as long as the newer pump which takes 48 minutes alone.
Explanation:
If an older pump takes 4 times as long to drain a pool as a newer pump, and together they take 4 hours to drain the pool, we can find out how long it would take for the older pump to drain the pool on its own by setting up an equation based on their rates of work.
Let's denote the time it takes for the newer pump to drain the pool alone as t hours. This means that the older pump would take 4t hours to do the job on its own.
Working together for one hour, they would collectively drain 1/t + 1/4t of the pool. Since they can drain the entire pool in 4 hours working together, we can write the equation:
1/t + 1/4t = 1/4
Now, solving for t:
4 + 1 = t
4t + t = 4t
5t = 4t
5t = 4
t = 4/5
So, the newer pump takes 4/5 of an hour (which is 48 minutes) to drain the pool alone. Then the older pump, taking 4 times as long, would take 4 * 4/5, which is 16/5 or 3.2 hours (which is 3 hours and 12 minutes) to drain the pool on its own.
Find the mean of the data set. If necessary round to nearest tenth. 18.1,17.9,16.8,18.7,15.1
-0.6, -5/8, -7/12, -0.72 least to greatest
what is The cost per unit?
Train A and train B leave a central station at the same time. They travel the same speed, but in opposite directions, with train A heading towards station A, and train B heading towards station B. Train A reaches station A after 4 h. Train B reaches station B after 312 h. Station A and Station B are 562.5 mi apart. What is the rate of the trains? Enter your answer in the box.
the answer is 75 mph i took the test and it said 75 not 1.78
Answer:
its 75 i did the math a calaculator
Step-by-step explanation:
The ordered pair (–2, –4) is a solution of which system?
The given ordered pair is the solution of y ≤ x + 2 and y ≥ x - 3. Option E is correct.
As of the given numeral, The ordered pair (–2, –4) is a solution of which system is to be determined.
What is inequality?Inequality is defined as the relationship of an equation containing the symbol ( ≤, ≥, <, >) instead of the equal sign.
here,
(–2, –4) is a solution of y ≤ x + 2 and y ≥ x - 3,
Proof,
Substitute this ordered paired in the inequality,
-4 ≤ -2 + 2
-4 < 0
and
-4 ≥ -2 - 3
-4 > -5
Thus, the ordered pair supplied is the solution of y x + 2 and y x - 3. Option E is the right answer.
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F(x)=x-2/x^3+x find the domain
Compound interest £2000 for 3 years 5.5% annum
5 minus the product of V and 7
2) Mr. Somers had twenty pieces of metal that were all the same length. If each piece of metal was 3 1/5 inches long and he put them side by side, what would be the total length of all the pieces together?
Find an equation for the line with the given properties. Express the equation in slope-intercept form. Containing the points Upper P equals (-1, 3) and Upper Q equals (1, 0)
358=15n+85 what does n equal
3/5 of 40 dollar restaurant
june is working on an addition problem and starts with 17,985. after she adds, she still has 17,985. which property od addition did june use
So is the answer - least is the negative first, them zero, them the positive?
One positive number is 1/5 of another number. The difference between the two numbers is 60. Find the numbers.
Answer:
15 and 75Step-by-step explanation:
[tex]n-second\ number\\\\\dfrac{1}{5}n-first\ number\\\\n-\dfrac{1}{5}n=\dfrac{4}{5}n-difference\ between\ the\ two\ numbers\\\\\text{Equation:}\\\\\dfrac{4}{5}n=60\qquad\text{multiply both sides ny 5}\\\\\not5\cdot\dfrac{4}{\not5}n=(5)(60)\\\\4n=300\qquad\text{divide both sides by 4}\\\\\dfrac{4\!\!\!\!\diagup n}{4\!\!\!\!\diagup}=\dfrac{300}{4}\\\\n=75\\\\\dfrac{1}{5}n=\left(\dfrac{1}{5}\right)(75)=\dfrac{75}{5}=15[/tex]
The two positive numbers are 15 and 75 respectively.
What is an expression?
Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Let the two numbers be x and y respectively. Now let corelate the statement given in question :
One positive number is 1/5 of another number which means x=(1/5) y
and, it is also given that the difference between the two numbers is 60 which means y -x = 60. Now solving these question by substitution method.
y-x = 60
5x-x= 60
4x = 60
x = 15
y = 75
Therefore, the two positive numbers are 15 and 75 respectively.
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is 11:17 equivalent to 17:11
Answer:
No
Step-by-step explanation:
If these are time values, ...
11:17 is about 5 hours 54 minutes earlier than 17:11.
___
If these are ratios, ...
11/17 is less than 1, whereas 17/11 is greater than 1
Each is the inverse of the other.
Find parametric equations for the line through the point ( 0,3,2 ) that is perpendicular to the line ! ! x =1+t , ! ! ! y = 3−t , ! ! z = 4t , and intersects this line. (use the parameter t ).
Ceremonies help individuals cope with loss as they facilitate the grieving process. Please select the best answer from the choices provided. T F
Answer:
True
Step-by-step explanation:
Ceremonies do help individuals cope with loss as they facilitate the grieving process.
Solve the equation 6x + 3y = 15 for y. What does y equal if x = 2? If x = 5?
Find the determinant of the n×n matrix a with 's on the diagonal, 's above the diagonal, and 's below the diagonal
Suppose that it costs $25 to place a classified advertisement in the newspaper, plus $3 for each line. Then the cost to place an ad x lines long is given by y dollars, where y=3x+25. Express an ordered pair the fact that a 2 line ad cost $31
Over last week,the daily low temperature in degrees Fahrenheit have been -4,6.2,18 1/2,-5.9,-1/4,and1.75.list these numbers in order from least to greatest
Country A produces about eight times the amount of diamonds in carats produced in country B. If the total produced in both countries is 9,000,000 carats, find the amount produced in each country
Find a parametric representation of the solution set of the linear equation. (enter your answer as a comma-separated list of equations. use s and t as your parameters.) x + y + z = 2
The parametric representation of the solution set for the equation x + y + z = 2 is x = t, y = 2 - s - t, z = s, with 's' and 't' as the parameters.
Explanation:To find the parametric representation of the solution set of the linear equation x + y + z = 2, we first need to express two variables in terms of the third. Let's use 's' and 't' as parameters.
We can express x and y in terms of z. Let's express z as 's'. So, z = s.
The equation x + y + z = 2 thus becomes x + y = 2 - s. We can choose x = t and y = 2 - s - t.
So, the parametric representation of the solution set for the given linear equation is (x = t, y = 2 - s - t, z = s), where 's' and 't' are parameters that can assume any real value.
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ymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is
C(x) = 3250 + 5x + 0.1x2 (0 ≤ x ≤ 500).
Gymnast Clothing sells the cleats at $110 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit?
Ms. Ache is paid $1250 per week but it's fined $100 each day she is late to work Ms.A che wants to make at least $3,000 over the next three weeks so she can take a vacation. over the next three weeks, what is the maximum number of days she can be late to work and still reach her goal of making at least $3000?
Answer:
7 days
Step-by-step explanation:
Given: Ms. Ache is paid $1250 per week but it's fined $100 each day she is late to work.
To Find: maximum number of days she can be late to work and still reach her goal of making at least $3000?
Solution:
per week payment of Ms. Ache =[tex]\$[/tex] [tex]1250[/tex]
Fine for getting late a day = [tex]\$[/tex] [tex]100[/tex]
let number of days Ms. Ache gets late = [tex]\text{x}[/tex]
Amount Ms. Ache wants to make in three weeks = [tex]\$[/tex] [tex]3000[/tex]
maximum earning potential of Ms. Ache in 3 weeks = [tex]1250\times3[/tex]= [tex]\$[/tex] [tex]3750[/tex]
Net earning = maximum earning potential of Ms. Ache in 3 weeks - total fine
=[tex]\$ 3750 - 100\text{x}[/tex]
To reach a goal of [tex]\$[/tex] [tex]3000[/tex]
[tex]\$ 3750 - 100\text{x}[/tex] ≥ [tex]3000[/tex]
[tex]100\text{x}[/tex]≤[tex]750[/tex]
[tex]\text{x}\leq 7[/tex]
Maximum number of days she can be late to work and still reach her goal of making at least $3000 is [tex]7[/tex] [tex]\text{days}[/tex]
A couple has 4 children. what is the probability they would have four boys
Which of the following is not an isometry?
rotation
dilation
translation
Answer:
B. Dilation.
Step-by-step explanation:
We are asked to find which transformation is not isometric.
We know that isometry preserves length.
We know that the length of a figure remains unchanged after rotation and dilation as they preserves length.
We also know that dilation either enlarges length or shrinks length of a figure, therefore, the correct choice is dilation.
A line passes through the point (d, d) and has a slope of k. Which equation models the line?
Evaluate. 7^2 - 3 + 9 × 8 ÷ 2
w =