At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
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.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
