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.)

Guest Nov 16, 2018

#2**+1 **

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.**

Guest Nov 16, 2018