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If Rachel were to paint her living room alone, it would take 2 hours. Her sister Fran could do the job in 5 hours. How many hours would it take them working together?
Express your answer as a fraction reduced to lowest terms, if needed.


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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