Question 1195970
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Ben and Jun can finish repairing a computer in 3 hrs. 
If it takes Ben working alone 2 hours longer than Jun working alone, 
how many hours will each can finish the work alone?
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<pre>
Let x be the time in hours for Jun to complete the job working alone.

Then that time for Ben is (x+2) hours.


In one hour, Jun makes  {{{1/x}}}  part of the job, working alone;

             Ben makes  {{{1/(x+2)}}}  part of the job.


Working together, they make  {{{1/x}}} + {{{1/(x+2)}}}  part of the job.

According to the condition, it is equal  {{{1/3}}}  part of the job.


So, you have this equation

    {{{1/x}}} + {{{1/(x+2)}}} = {{{1/3}}}.


Your goal is to solve it and to get x as the solution of this equation.


To solve it, multiply both sides by 3*x*(x+2).  You will get then

    3*(x+2) + 3x = x*(x+2)

    3x + 6 + 3x = x^2 + 2x

    x^2 -4x - 6 = 0


Use the quadratic formula

    {{{x[1,2]}}} = {{{(4 +- sqrt((-4)^2 - 4*1*(-6)))/2}}} = {{{(4 +- sqrt(40))/2}}} = {{{2 +- sqrt(10)}}}.


The roots are  {{{x[1]}}} = {{{2+sqrt(10)}}} = 5.16228,  {{{x[2]}}} = -1.16228.


We ignore the negative root and accept the positive one.


<U>ANSWER</U>.  It will take Jun 5.16228 hours to complete the job working alone,

                      and 7.16228 hours for Ben to complete the job working alone.


<U>CHECK</U>.  {{{1/5.16228}}} + {{{1/7.16228}}} = 0.33333  of the job = {{{1/3}}} of the job.

        The answer is correct.
</pre>

Solved.