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Sagot :
Rachel and her sister Fran together can paint the living room in [tex]\frac{10}{7}[/tex] hours
Given that
Rachel can paint half of the living room in 1 hour
Fran can paint [tex]\frac{1}{5}[/tex]th part of the living room in 1 hour
Let's assume together they paint the living room in x hours
⇒ together they can paint [tex]\frac{1}{x}[/tex]th part of the living room in 1 hour
By proportions,
⇒[tex]\frac{1}{2}[/tex]+[tex]\frac{1}{5}[/tex]= [tex]\frac{1}{x}[/tex] {using operation proportions and addition}
⇒[tex]\frac{7}{10}[/tex]=[tex]\frac{1}{x}[/tex]
⇒x=[tex]\frac{10}{7}[/tex]
⇒ together they can paint [tex]\frac{7}{10}[/tex]th part of the living room in 1 hour
It means, Rachel and her sister Fran together can paint the living room in [tex]\frac{10}{7}[/tex] hours
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