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Sagot :
Answer:
B. Calculate how many hours it takes each to fill the pool
Step-by-step explanation:
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 [tex]\bf{\dfrac{1}{x}}[/tex] parts of the pool and B will fill [tex]\bf{\dfrac{1}{x+3}}[/tex] parts. Since using both hoses fills the pool completely, you have to:
[tex]\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{$\begin{gathered}\sf \bf{ \ \ \ =\frac{2x+2x+6}{x(x+3)} } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x^2+3x=4x+6\ \Longrightarrow\ \ 0=x^2-x-6=(x-3)(x+2) } \end{gathered}$}[/tex]
Hose A takes 3 hours to fill the pool and Hose B takes 6 hours.
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