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?Answer10. Refer to problem 9. If each woman filled the order for 30 dresses by herself, how manymore days would it take Alberta Emery?AnswerSteung can

Answer 1

#9

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,

$(\frac{1}{3}+\frac{1}{2}_{})t=30$

Solving for "t", we get,

$\begin{gathered} (\frac{1}{3}+\frac{1}{2}_{})t=30 \\ (\frac{2}{6}+\frac{3}{6})t=30 \\ \frac{5}{6}t=30 \\ t=\frac{30}{\frac{5}{6}} \\ t=30\times\frac{6}{5} \\ t=\frac{180}{5} \\ t=36 \end{gathered}$

So, it will take them 36 days to sew 30 dresses if they work together.