Question

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 many hours it takes each to fill the pool.

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

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.