Given that Alberta Emery can sew 1 dress in 3 days. so the efficiency of Alverta Emery is given by,
[tex]=\frac{1}{3}\text{ work per day}[/tex]
Similarly, given that Allison Taylor takes 2 days to sew 1 dress, so the efficiency of Allison Taylor is given by,
[tex]=\frac{1}{2}\text{ work per day}[/tex]
When they combine their efforts, the amount of work done per day is given by,
[tex]\begin{gathered} =\frac{1}{3}+\frac{1}{2} \\ =\frac{2+3}{6} \\ =\frac{5}{6}\text{ work per day} \end{gathered}[/tex]
So the number of days required to sew 30 dresses when both of them work together, is calculated as,
[tex]\begin{gathered} =\frac{30}{\frac{5}{6}} \\ =30\cdot\frac{6}{5} \\ =6\cdot6 \\ =36 \end{gathered}[/tex]
Thus, they will take 36 days to sew 30 dresses.
