We know rate and time are inverses of each other.
Let's take the inverse of each time to find their rates.
Alberta Emery
It takes her 3 days to sew a dress. So, her rate is 1/3
Allison Taylor
It takes her 2 days to sew a dress. So, her rate is 1/2
Their combined rate (when working together) is '1/3 + 1/2'
We know
rate x time = job completed
We can use the combined rate (just found) and jobs = 30 dress, to find the time it will take both of them working together to sew 30 dresses.
The equation is,
[tex](\frac{1}{3}+\frac{1}{2}_{})t=30[/tex]Solving for "t", we get,
[tex]\begin{gathered} (\frac{1}{3}+\frac{1}{2}_{})t=30 \\ (\frac{2}{6}+\frac{3}{6})t=30 \\ \frac{5}{6}t=30 \\ t=\frac{30}{\frac{5}{6}} \\ t=30\times\frac{6}{5} \\ t=\frac{180}{5} \\ t=36 \end{gathered}[/tex]So, it will take them 36 days to sew 30 dresses if they work together.