Question

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.

Answer 1

Rachel and her sister Fran together can paint the living room in $\frac{10}{7}$ hours

Given that

Rachel can paint half of the living room in 1 hour

Fran can paint $\frac{1}{5}$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 $\frac{1}{x}$th part of the living room in 1 hour

By proportions,

⇒$\frac{1}{2}$+$\frac{1}{5}$= $\frac{1}{x}$ {using operation proportions and addition}

⇒$\frac{7}{10}$=$\frac{1}{x}$

⇒x=$\frac{10}{7}$        

⇒ together they can paint $\frac{7}{10}$th part of the living room in 1 hour

It means, Rachel and her sister Fran together can paint the living room in $\frac{10}{7}$ hours

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