Two companies working together can clear a parcel of land in 24 hours. Working alone, it would take Company A 2 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 time taken by Co. B = B, then:
The time taken by Co. A = B+2
1/B + 1/(B+2) =1/24, solve for B
Solve for B:
1/B + 1/(B + 2) = 1/24
Bring 1/B + 1/(B + 2) together using the common denominator B (B + 2):
(2 (B + 1))/(B (B + 2)) = 1/24
Cross multiply:
48 (B + 1) = B (B + 2)
Expand out terms of the left hand side:
48 B + 48 = B (B + 2)
Expand out terms of the right hand side:
48 B + 48 = B^2 + 2 B
Subtract B^2 + 2 B from both sides:
-B^2 + 46 B + 48 = 0
Multiply both sides by -1:
B^2 - 46 B - 48 = 0
By using the Quaratic Formula, we have:
B = 23 + sqrt(577)- Hours and A = 25 + sqrt(577)- Hours.
