Passage

Directions: The data below represents the number of people required for various project to be completed in different number of days. Use this information to answer the question asked. Project Situation I Situation II Number of Workers Number of Days Required Number of Workers Number of Days Required P 1 x (x + 5) (x – 5) (x + 15) P 2 y (y + 10) 40 (y – 5) P 3 50 z 80 (y – 10) P 4 y (z – 1) (x + 10) (z – 4)

In a group A, if the total number of workers is (0.2x × 0.8y), then what is the number of days required by group A to complete Project P_2, given y > 15?

From the data for Project P2, we have 40 times (y minus 5) equals y times (y + 10). This simplifies to 40y minus 200 equals y squared + 10y, which factors as y squared minus 30y plus 200 equals 0. The valid root for y greater than 15 is y equals 20. Thus, the work for Project P2 is 20 workers multiplied by 30 days, giving 600 units. The total workers in group A is 0.2 times 5 multiplied by 0.8 times 20, which equals 16 multiplied by 20, equaling 48 workers. The required days to complete the project is 600 divided by 48, which gives 12.5.

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