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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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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 part of the job, working alone;
Ben makes part of the job.
Working together, they make + part of the job.
According to the condition, it is equal part of the job.
So, you have this equation
+ = .
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
= = = .
The roots are = = 5.16228, = -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. + = 0.33333 of the job = of the job.
The answer is correct.
Solved.