Question 1162729
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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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<pre>
Let x be the time for company B; then the time for company A is x+10.


The setup equation is


    {{{1/x}}} + {{{1/(x+10)}}} = {{{1/15}}}


saying that the combined rate of work of the two companies is  {{{1/15}}}  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[1,2]}}} = {{{(20 +- sqrt(20^2 + 4*150))/2}}} = {{{(20 +- sqrt(1000))/2}}} = {{{(20 +- 10*sqrt(10))/2}}} = {{{10 +- 5*sqrt(10)}}}.



Of the two roots, only positive value x= {{{10 + 5*sqrt(10)}}} =  25.811 hours is the meaningfull solution.


<U>ANSWER</U>.  25.811 hours for company B  and  25.811+10 = 35.811 hours for company A.


<U>CHECK</U>.   Check the combined rate of work  {{{1/25.811}}} + {{{1/35.811}}} = 0.0666667 hours.  {{{1/15}}} = 0.0666667 hours.

         ! Precisely/accurately correct !
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Solved.