Question

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?

Answer 1

9514 1404 393

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

__

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.