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A pitchers earned-run average E varies directly as the number R of earned runs allowed and inversely as the number of I innings pitched. A certain pitcher had an earned-run average of 2.92, giving up 85 earned runs in 262 innings. How many earned runs would the pitcher have given up having pitched 311 innings with the same average?

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sqdancefan

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Answer:

  101 runs

Step-by-step explanation:

The given relation is ...

  E = kR/I

The value of k can be found from the given numbers.

  2.92 = k(85/262)

  k = 2.92(262/85) = 9

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Solving the above equation for R, we get ...

  R = E·I/9 = (2.92)(311)/9 = 100.9 ≈ 101

The pitcher would have given up 101 earned runs in 311 innings.

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