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# help please! (algebra rate problem)

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Rowena can paint a room in $$14$$ hours, while Ruby can paint it in $$6$$ hours. If Rowena paints for $$x$$ hours and Ruby paints for $$y$$ hours, they will finish half of the painting, while if Rowena paints for $$y$$ hours and Ruby paints for $$x$$ hours they will paint the whole room. Find the ordered pair $$(x, y)$$.

Mar 18, 2019

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$$r_{row}=\dfrac{1rm}{14hr}\\ r_{rub}=\dfrac{1rm}{6hr}\\ x \cdot r_{row} + y \cdot r_{rub} = \dfrac 1 2\\ y \cdot r_{row} + x \cdot r_{rub} = 1\\ \dfrac{x}{14} + \dfrac{y}{6} = \dfrac 1 2\\ \dfrac{y}{14} + \dfrac{x}{6} = 1$$

Do you think you can solve it from here?

Mar 18, 2019
edited by Rom  Mar 18, 2019