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23 July, 19:36

Jake can cut and split a cord of firewood in 9 fewer hours than Dwight can. When they work together, it takes them 6 hours. How long would it take each of them to do the job alone?

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  1. 23 July, 19:57
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    18 hours for Dwight, 9 hours for Jake

    Step-by-step explanation:

    If J is the time it takes for Jake working alone, and D is the time it takes for Dwight working alone, then:

    J = D - 9

    Working together, Jake's speed plus Dwight's speed equals 1 cord per 6 hours.

    1 / J + 1 / D = 1 / 6

    Solve the system of equations by substituting for J:

    1 / (D - 9) + 1 / D = 1 / 6

    Multiply both sides by D - 9.

    1 + (D - 9) / D = (D - 9) / 6

    Multiply both sides by D:

    D + D - 9 = D (D - 9) / 6

    Simplify and solve:

    2D - 9 = (D² - 9D) / 6

    12D - 54 = D² - 9D

    0 = D² - 21D + 54

    0 = (D - 3) (D - 18)

    D = 3 or 18

    Since J = D - 9, D must be greater than 9. So D = 18 and J = 9.

    That means it takes Dwight 18 hours working alone, and it takes Jake 9 hours working alone.
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