SOLUTION: Gabo can do a job in one hour less then Wynter. If Gabo and Wynter work together the job takes 6/5 hours.How long would it take each person working alone?

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Question 1171787: Gabo can do a job in one hour less then Wynter. If Gabo and Wynter work together the job takes 6/5 hours.How long would it take each person working alone?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39631)   (Show Source): You can put this solution on YOUR website!
Time for Gabo to do 1 job, w-1.
Time for Wynter to do 1 job, w.

---------------solve,...
Answer by ikleyn(52932)   (Show Source): You can put this solution on YOUR website!
.

            In his post,  @josgarithmetic offers you to solve this equation  .

            This equation is  INCORRECT,  so you better  IGNORE  it, for your safety : . 


The correct equation is

     +  = ,


or, equivalently,

     +  = .      (1)


At this point a person familiar with arithmetic operations on fractions just can to guess the solution

w= 3,  since   +  = .



But if you want to have full formal algebraic solution, let's do it step by step.



Multiply equation (1) by 6w*(w-1)  (both sides).   You will get then 


    6w + 6*(w-1) = 5w*(w-1)

    6w + 6w - 6 = 5w^2 - 5w

    5w^2 - 17w + 7 = 0

    (w-3)*(5w+2) = 0.


It has two roots, one positive and one negative.

Only positive root w= 3 is the solution to the problem,

confirming that my earlier guess was correct.


ANSWER.  Winter makes the job in 3 hours;  Gabo makes it in 2 hours.

----------------

To see other similar solved problems, look into the lesson
    - Using quadratic equations to solve word problems on joint work
in this site.

Learn the subject from there.


Happy learning (!)


/\/\/\/\/\/\/\/

After my notice, @josgarithmetic changed his post.



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