In Arizona, where there are 334 sunny days per year, it requires 319 acres of land to generate 300 MW of average annual power. If there are only 170 sunny days per year in Pennsylvania, how many acres of land would it require to generate the same average annual power? Please round to the nearest acre. Note: assume that a cloudy day delivers 0 watts/acre of solar power. This is not true, but it simplifies the problem for us.
Question
In Arizona, where there are 334 sunny days per year, it requires 319 acres of land to generate 300 MW of average annual power. If there are only 170 sunny days per year in Pennsylvania, how many acres of land would it require to generate the same average annual power? Please round to the nearest acre. Note: assume that a cloudy day delivers 0 watts/acre of solar power. This is not true, but it simplifies the problem for us.
Solution
To solve this problem, we first need to understand that the amount of solar power generated is directly proportional to the number of sunny days.
In Arizona, 319 acres of land generate 300 MW of power in 334 sunny days. So, the power generated per acre per sunny day is 300 MW / 319 acres / 334 days = 0.0028 MW/acre/day.
In Pennsylvania, there are only 170 sunny days per year. To find out how many acres are needed to generate the same 300 MW of power, we can set up the following equation:
0.0028 MW/acre/day * 170 days * X acres = 300 MW
Solving for X gives us X = 300 MW / (0.0028 MW/acre/day * 170 days) = 63571.43 acres.
Rounding to the nearest acre, it would require approximately 63571 acres of land in Pennsylvania to generate the same average annual power as in Arizona.
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