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Answer :
We determine the time taken by Morgan to make one cabinet when working alone compared to Donna. Through solving the given equation, we find that Donna takes 12 hours to make one cabinet by herself.
Morgan: x + 8 hours per cabinet
Donna: x hours per cabinet
Total time working together: 3 hours per cabinet
Equation: 1/(x+8) + 1/x = 1/3
After solving the equation, we find that x = 12 hours for Donna to make one cabinet.
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For Morgan to make one cabinet by alone, it will take 12 hours.
Representing the problem Mathematically
Assuming Donna takes "x" hours to make one cabinet.
Morgan takes 8 more hours
Then , Donna = "x + 8" hours to make one cabinet.
Working together , time taken = 3 hours.
We can set up an equation based on their rates of work:
1/(x + 8) + 1/x = 1/3
(1 * x + 1 * (x + 8)) / ((x + 8) * x) = 1/3
(x + x + 8) / (x² + 8x) = 1/3
(2x + 8) / (x² + 8x) = 1/3
3(2x + 8) = x² + 8x
6x + 24 = x² + 8x
Rearranging the equation:
x² + 2x - 24 = 0
Now we can factor or use the quadratic formula to solve for "x." Factoring the equation:
(x + 6)(x - 4) = 0
x + 6 = 0 or x - 4 = 0
x = -6 or x = 4
Since we are considering time, the solution cannot be negative. Therefore, x = 4, which means it takes Donna 4 hours to make one cabinet.
Morgan's time = 4 + 8 = 12 hours
Therefore, it takes Morgan 12 hours to make one cabinet by herself.
Learn more on equations: https://brainly.com/question/29133548
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