Three people who work full-time are to work together on a prooject, but their total time on the project is to be equivalent to that of only one person working fuIl-time. If one of the people is budgeted for one-half of his time to the project anda second person for one- third of her time, what part of the third worker's time should be budgetedto this project? 13.3% 35.2% 16.7% 18.7%

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Denote Total Time: Let's denote the total time of one person working full-time as T. The first person is budgeted for one-half of his time, so that's (1/2)T. The second person is budgeted for one-third of her time, so that's (1/3)T. We need to find the fraction of time the third person should contribute, let's call it xT, such that the sum of their times is equal to T.Set Up Equation: We can set up the equation: (1/2)T + (1/3)T + xT = T. This equation represents the total time contributed by all three workers being equivalent to one full-time worker.Find Common Denominator: To solve for x, we first need to find a common denominator for the fractions. The common denominator for 2 and 3 is 6. So we convert the fractions: (3/6)T + (2/6)T + xT = T.Combine Fractions: Now we combine the fractions: (3/6 + 2/6)T + xT = T. Simplifying the fractions we get: (5/6)T + xT = T.Isolate xT: Subtract (5/6)T from both sides to isolate xT: xT = T - (5/6)T.Calculate Difference: Now we calculate T - (5/6)T. This is equal to (1 - 5/6)T, which simplifies to (1/6)T.Calculate Fraction: Therefore, xT = (1/6)T. This means that x, the fraction of the third worker's time, is 1/6.Express as Percentage: To express x as a percentage, we multiply by 100: x * 100 = (1/6) * 100 = 16.7%.

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