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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

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