SOLUTION: 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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Question 1195970: 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?
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~

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%2Fx  part of the job, working alone;

             Ben makes  1%2F%28x%2B2%29  part of the job.


Working together, they make  1%2Fx + 1%2F%28x%2B2%29  part of the job.

According to the condition, it is equal  1%2F3  part of the job.


So, you have this equation

    1%2Fx + 1%2F%28x%2B2%29 = 1%2F3.


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%5B1%2C2%5D = %284+%2B-+sqrt%28%28-4%29%5E2+-+4%2A1%2A%28-6%29%29%29%2F2 = %284+%2B-+sqrt%2840%29%29%2F2 = 2+%2B-+sqrt%2810%29.


The roots are  x%5B1%5D = 2%2Bsqrt%2810%29 = 5.16228,  x%5B2%5D = -1.16228.


We ignore the negative root and accept the positive one.


ANSWER.  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.


CHECK.  1%2F5.16228 + 1%2F7.16228 = 0.33333  of the job = 1%2F3 of the job.

        The answer is correct.

Solved.



Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
j, the time for Jun to do the repair job by himself
(j+2), the time for Ben to do the job by himself

highlight_green%281%2Fj%2B1%2F%28j%2B2%29=1%2F3%29
3j%28j%2B2%29%281%2Fj%2B1%2F%28j%2B2%29%29=3j%28j%2B2%29%281%2F3%29
3%28j%2B2%29%2B3j=j%28j%2B2%29
3j%2B6%2B3j=j%5E2%2B2j
6j%2B6=j%5E2%2B2j
highlight_green%28j%5E2-4j-6=0%29

j=%284%2B-+sqrt%2816-4%28-6%29%29%29%2F2
j=%284%2B-+sqrt%2840%29%29%2F2
j=%284%2B-+2%2Asqrt%2810%29%29%2F2
highlight%28j=2%2Bsqrt%2810%29%29-----------time in hours for Jun working alone
-
highlight%284%2Bsqrt%2810%29%29------------time for Ben, working alone