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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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One of the roots of the quadratic equation 4mnx^2 – 6m^2x – 6n^2x + 9mn = 0 (m, n ≠ 0) is a)-3m/2n b)3m/2n c)2m/3n d)-2m/3n
maxonik [38]

Answer:

B.\ \frac{3m}{2n}

Step-by-step explanation:

Given

4mnx^2 - 6m^2x - 6n^2x + 9mn = 0\ (m, n \neq  0)

Required

Calculate one of the root of the equation

4mnx^2 - 6m^2x - 6n^2x + 9mn = 0

Factorize

2mx(2nx - 3m) -3n(2nx - 3m) = 0

(2mx - 3n)(2nx - 3m) = 0

Split equation

2mx - 3n = 0\ or\ 2nx - 3m = 0

Make x the subject of formula in both expressions

2mx = 3n\ or\ 2nx = 3m

x = \frac{3n}{2m}\ or\ x = \frac{3m}{2n}

<em>From the list of given options, one of the roots of the equation is</em> \frac{3m}{2n}

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The correct answers are the second option (Option B) and the last option (Option E).

 The explanation is shown below:

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 2. The Option B has the following common ratio:

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 r=1.5

 3. The Option E has the following common ratio:

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 r=-5

6 0
2 years ago
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