.
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?
~~~~~~~~~~~~~~~~~~~~~
Let "z" be the time for Zoe, in hours; then the time for Mark is (z+2) hours.
The total job equation is
+ + = 1 job,
or
+ = 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.