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# help

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One painter can paint an Italian restaurant in 10 hours and the second painter takes 8 hours. How long would it take the two painters together to paint the Italian restaurant?

Apr 2, 2020

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One painter can paint an Italian restaurant in 10 hours and the second painter takes 8 hours.
How long would it take the two painters together to paint the Italian restaurant (R)?

$$\begin{array}{|rcll|} \hline \mathbf{\dfrac{R}{10\ h} + \dfrac{R}{8\ h}} &=& \mathbf{ \dfrac{R}{x} } \\\\ \dfrac{1}{10} + \dfrac{1}{8} &=& \dfrac{1}{x} \quad | \quad \times 80x \\\\ \dfrac{80x}{10} + \dfrac{80x}{8} &=& \dfrac{80x}{x} \\\\ 8x+10x &=& 80 \\\\ 18x &=& 80 \\\\ x &=& \dfrac{80}{18} \\\\ x &=& 4.\overline{4}\ \text{hours} \\\\ \mathbf{x} &=& \mathbf{4\ \text{hours}\ 26 \ \text{minutes}\ 40 \ \text{seconds} } \\ \hline \end{array}$$

Apr 2, 2020