Two companies working together can clear a parcel of land in 8 hours. Working alone, it would take Company A 5 hours longer to clear the land than it would Company B. How long would it take Company B to clear the parcel of land alone? (Round your answer to the nearest tenth.)
Let the hourly rate of company B = 1/B
Then, the hourly rate of company A =1 /(B + 5)
1/B + 1 / (B+5) = 1/8, solve for B
Solve for B:
1/B + 1/(B + 5) = 1/8
Bring 1/B + 1/(B + 5) together using the common denominator B (B + 5):
(2 B + 5)/(B (B + 5)) = 1/8
Cross multiply:
8 (2 B + 5) = B (B + 5)
Expand out terms of the left hand side:
16 B + 40 = B (B + 5)
Expand out terms of the right hand side:
16 B + 40 = B^2 + 5 B
Subtract B^2 + 5 B from both sides:
-B^2 + 11 B + 40 = 0
Multiply both sides by -1:
B^2 - 11 B - 40 = 0
Add 40 to both sides:
B^2 - 11 B = 40
Add 121/4 to both sides:
B^2 - 11 B + 121/4 = 281/4
Write the left hand side as a square:
(B - 11/2)^2 = 281/4
Take the square root of both sides:
B - 11/2 = sqrt(281)/2 or B - 11/2 = -sqrt(281)/2
Add 11/2 to both sides:
B = 11/2 + sqrt(281)/2 or B - 11/2 = -sqrt(281)/2
Add 11/2 to both sides:
B = 11/2 + sqrt(281)/2 =13.882 =~13.9 hours for Co. B to finish the Job alone.
13.9 + 5 =~18.9 hours for Co. A to finish the Job alone
