SOLUTION: Two companies working together can clear a parcel of land in 18 hours. Working alone, it would take Company A 10 hours longer to clear the land than it would Company B. How long

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Two companies working together can clear a parcel of land in 18 hours. Working alone, it would take Company A 10 hours longer to clear the land than it would Company B. How long       Log On


   

Question 1178832: Two companies working together can clear a parcel of land in 18 hours. Working alone, it would take Company A 10 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.)
Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the number of hours company B alone would take; then x+10 is the number of hours it would take company A alone.

The fraction of the job company A does in 1 hour is 1/(x+10); the fraction company B does alone in 1 hour is 1/x. The fraction they do together in 1 hours is 1/18.

1%2F%28x%2B10%29%2B1%2Fx+=+1%2F18

Multiply everything by the least common denominator, 18(x)(x+10):

18%28x%29%2B18%28x%2B10%29+=+%28x%29%28x%2B10%29
36x%2B180+=+x%5E2%2B10x
x%5E2-26x-180+=+0

That quadratic is not factorable. Use the quadratic formula to get an exact answer in radical form, or a graphing calculator to get an approximate decimal answer.