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Sagot :
It takes about 13.33 hours for the friend to paint a room by himself.
If two persons are working on the same project together, their work rates add up and they can finish the project faster. If x is the time taken by person 1 to complete a task, then the work rate is 1/x. If y is the time taken by person 2 to complete a task, then the work rate is 1/y. Then, the formula to calculate the work-rate problem is [tex]\frac{1}{x}+\frac{1}{y}=\frac{1}{t}[/tex].
Here, the rate of work done by person 1 is 1/8. Together, the rate is 1/5. Then,
[tex]\begin{aligned}\frac{1}{8}+\frac{1}{y}&=\frac{1}{5}\\\frac{y+8}{8y}&=\frac{1}{5}\\5y+40&=8y\\3y&=40\\y&=\frac{40}{3}\\&=13.33\end{aligned}[/tex]
Therefore, the answer is 13.33 hours.
To know more about the work-rate problem:
https://brainly.com/question/8958704
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