Math CentralQuandaries & Queries


Question from a student:

At 100% efficiency two generators would produce 750 MW of power. At efficiencies of 65% and 75%, they produce 530 MW. At 100% efficiency, what power would each produce?


Suppose the first generator produces $x$ MW of power at 100% efficiency and the second generator produces $y$ MW of power at 100% efficiency. You then know that

\[x + y = 750.\]

At $65\%$ efficiency the first generator produces $0.65 \times x$ MW of power. How much power does the second generator produce at $75\%$ efficiency? The sum of thee is 530 MW. This give you a second equation in $x$ and $y.$

Solve the equations for $x$ and $y.$ Make sure you verify your answer.


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