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kykrilka [37]
1 year ago
11

Two hoses A and B together fill a swimming pool in two hours. A does it by herself in three hours less than B. Calculate how man

y hours it takes each to fill the pool.
Mathematics
2 answers:
Sunny_sXe [5.5K]1 year ago
7 0

If hose A takes x hours to fill the pool, hose B will take x+3 hours to fill the pool. So, each hour, A will fill \bf{\dfrac{1}{x}} parts of the pool and B will fill \bf{\dfrac{1}{x+3}} parts. Since using both hoses fills the pool completely, you have to:

                                                          \large\displaystyle\text{$\begin{gathered}\sf \bf{ 1= \frac{1}{x}+\frac{1}{x}+\frac{1}{x+3}+\frac{1}{x+3}     } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ =\frac{2}{x}+\frac{2}{x+3}   } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ =\frac{2x+2x+6}{x(x+3)} } \end{gathered}$}

\large\displaystyle\text{$\begin{gathered}\sf \bf{ x^2+3x=4x+6\ \Longrightarrow\ \ 0=x^2-x-6=(x-3)(x+2) } \end{gathered}$}

Hose A takes 3 hours to fill the pool and Hose B takes 6 hours.

Roman55 [17]1 year ago
4 0

Answer:

B. Calculate how many hours it takes each to fill the pool

Step-by-step explanation:

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If a= 11, solve for b and c.
oksian1 [2.3K]

Step-by-step explanation:

b = 11

c = 11✓2 because the properties of 45 45 90 triangle

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3 years ago
What are the coordinates of the intersection of the graphs of 3x - y^2 = 12 and y = -3
inessss [21]

Answer:

(7,-3)

Step-by-step explanation:

y = -3

substitute in the first equation

3x - y^2 = 12

3x - (-3)^2 = 12

3x - 9 = 12

3x = 12 + 9

3x = 21

x = 7

coordinates of intersection (7,-3)

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Lisa is a fitness instructor. For one month, she recorded the number of people who attended her aerobics class. She then used he
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3 years ago
A rectangle is 9 ft long and 40 in. wide. What is its<br> area in square feet?
Bad White [126]

Answer:

29.97 square feet

Step-by-step explanation:

Given

The length of rectangle = 9 ft

The width of rectangle = 40 in

We have to bring the length and width in same unit. As the area is required in square feet so we will convert width in feet

The width will be divided by 12 to be onverted into feet

So,

Width = 40/12 = 3.33 feet

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7 0
3 years ago
Read 2 more answers
What is the perimeter of quadrilateral ABCD with verticals at A(-11,-6) b(-3,0) c(1,0) and d (1,-6)
dedylja [7]

<u>Answer:</u>

32 units

<u>Step-by-step explanation:</u>

We have a quadrilateral ABCD and we are given the following coordinates for these vertices:

A (-11,-6)

B (-3,0)

C (1,0)

D (1,-6)

AB = \sqrt{(0-(-6))^2+(-3-(-11)^2} = \sqrt{36+64} =\sqrt{100} = 10 units

BC = \sqrt{(0-0)^2+(1-(-3)^2} = \sqrt{0+16} =\sqrt{16} = 4 units

CD = \sqrt{(0-(-6))^2+(1-1^2} = \sqrt{36+0} =\sqrt{36} = 6 units

AD = \sqrt{(-6-(-6))^2+(1-(-11)^2} = \sqrt{0+144} =\sqrt{144} = 12 units

Perimeter of ABCD = 10+4+6+12 = 32 units

6 0
3 years ago
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