SOLUTION: It takes Mark 2 hours longer to complete the promotional logo for a male business entrepreneur than it takes Zoe. The two of them work together for 3 hours then Zoe left, and Mark

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Question 1188418: It takes Mark 2 hours longer to complete the promotional logo for a male business entrepreneur than it takes Zoe. The two of them work together for 3 hours then Zoe left, and Mark finished the job in 1 hour. How long would it take each of them, working alone, to finish the job?
Answer by ikleyn(52788) About Me  (Show Source):
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It takes Mark 2 hours longer to complete the promotional logo for a male business entrepreneur
than it takes Zoe. The two of them work together for 3 hours then Zoe left,
and Mark finished the job in 1 hour. How long would it take each of them, working alone,
to finish the job?
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Let "z" be the time for Zoe, in hours;  then the time for Mark is (z+2) hours.


The total job equation is 


    3%2Fz + 3%2F%28z%2B2%29 + 1%2F%28z%2B2%29 = 1   job,

or

    3%2Fz + 4%2F%28z%2B2%29 = 1.


To solve it, multiply both sides by z*(z+2),  You will get


    3*(z+2) + 4z = z*(z+2)


Simplify


    3z + 6 + 4x = z^2 + 2z

    z^2 -5z - 6 = 0

    (z-6)*(z+1) = 0.


Of the two roots,  z= 6  and  z= -1, only positive value z= 6 is the solution to the problem.


ANSWER.  6 hours for Zoe and (6+2) = 8 hours for Mark.

Solved.