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?

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.