SOLUTION: Two companies working together can clear a parcel of land in 15 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 Equations Lessons -> SOLUTION: Two companies working together can clear a parcel of land in 15 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 1162729: Two companies working together can clear a parcel of land in 15 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.)
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
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Two companies working together can clear a parcel of land in 15 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?
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Let x be the time for company B; then the time for company A is x+10.


The setup equation is


    1%2Fx + 1%2F%28x%2B10%29 = 1%2F15


saying that the combined rate of work of the two companies is  1%2F15  of the job per hour.


To solve the equation, multiply both sides by 15x*(x+10).  You will get

    15*(x+10) + 15x = x*(x+10).


Simplify it step by step

    15x + 150 + 15x = x^2 + 10x

    30x + 150 = x^2 + 10x

    x^2 - 20x - 150 = 0


Use the quadratic formula

    x%5B1%2C2%5D = %2820+%2B-+sqrt%2820%5E2+%2B+4%2A150%29%29%2F2 = %2820+%2B-+sqrt%281000%29%29%2F2 = %2820+%2B-+10%2Asqrt%2810%29%29%2F2 = 10+%2B-+5%2Asqrt%2810%29.



Of the two roots, only positive value x= 10+%2B+5%2Asqrt%2810%29 =  25.811 hours is the meaningfull solution.


ANSWER.  25.811 hours for company B  and  25.811+10 = 35.811 hours for company A.


CHECK.   Check the combined rate of work  1%2F25.811 + 1%2F35.811 = 0.0666667 hours.  1%2F15 = 0.0666667 hours.

         ! Precisely/accurately correct !

Solved.



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1/15 = 0.666667 hours.
! Precisely/accurately correct !
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Close.
1/15 = 0.0666667 hours.