Answer:
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.
