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Consider $\"\"$ is the Beth $\"\"$ s time working alone, $\"\"$ is the Bills time working alone and $\"\"$ is the Edies time working alone.

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The part of the work done in one hour by three painters is $\"\"$ .

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The three painters working together and complete the one work in $\"\"$ .

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Hence $\"\"$

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$\"\"$

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Bill and Edie together can complete the work in $\"\"$ .

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$\"\"$

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$\"\"$ .

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One day, all three worked in $\"\"$ after Edie left, Beth and Bill required eight more hours to finish the work.

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$\"\"$

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$\"\"$ .

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The system of equations are $\"\"$

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Multiply the equation $\"\"$ by $\"\"$ and add to the equation $\"\"$ to eliminate $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in equation $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Multiply the equation $\"\"$ by $\"\"$ and add to the equation $\"\"$ to eliminate $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore, Beth work alone in $\"\"$ , Bill in $\"\"$ and Edie in $\"\"$ to complete the work.

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Beth work alone in $\"\"$ , Bill in $\"\"$ and Edie in $\"\"$ to complete the work.