Answer
It will take Melissa and Zack $2\frac{2}{9}$ hours to clean the house together.
Thus, they cannot finish the job before the movie starts.
Work Step by Step
Let
$x$= number of hours it will take them to clean the house together
Since Melissa can clean the house by herself in $4$ hours, then she can clean $\frac{1}{4}$ of the house in an hour.
Zack can clean the house by himself in 5 hours so he can clean $\frac{1}{5}$ of the house in an hour.
Thus, if they work together, they will be able to clean $\frac{1}{4} + \frac{1}{5}=\frac{9}{20}$ of the house in an hour.
Therefore, to find the time it will take them to clean the entire house working together, solve the equation $\frac{9}{20} \cdot x = 1$, to obtain:
$\frac{9}{20}x = 1
\\\frac{9}{20}x \cdot \frac{20}{9} = 1 \cdot \frac{20}{9}
\\x = \frac{20}{9}
\\x=2\frac{2}{9}$
Together, it will take Melissa and her husband $2\frac{2}{9}$ hours to clean the house. Since the movie will start in 2 hours, they won't finish before the movie starts.
