Question

9. Alberta Emery can sew a dress in 3 days. Allison Taylor requires only 2 days. If theycombine efforts to fill one order to sew 30 dresses, how long will they take to fill the order?Answer

Answer 1

Given that Alberta Emery can sew 1 dress in 3 days. so the efficiency of Alverta Emery is given by,

`=(1)/(3)\text{ work per day}`

Similarly, given that Allison Taylor takes 2 days to sew 1 dress, so the efficiency of Allison Taylor is given by,

`=(1)/(2)\text{ work per day}`

When they combine their efforts, the amount of work done per day is given by,

`\begin{gathered} =(1)/(3)+(1)/(2) \\ =(2+3)/(6) \\ =(5)/(6)\text{ work per day} \end{gathered}`

So the number of days required to sew 30 dresses when both of them work together, is calculated as,

`\begin{gathered} =(30)/((5)/(6)) \\ =30\cdot(6)/(5) \\ =6\cdot6 \\ =36 \end{gathered}`

Thus, they will take 36 days to sew 30 dresses.