Using the together rate, it is found that it would take them 16 hours to sew 12 dresses.
What is the together rate?
The together rate is the sum of each separate rate.
In this problem, we have that:
Hence, the together rate is the time it would take them to produce one dress working together, and is given by:
[tex]\frac{1}{x} = \frac{1}{2} + \frac{1}{4}[/tex]
[tex]\frac{1}{x} = \frac{2 + 1}{4}[/tex]
[tex]3x = 4[/tex]
[tex]x = \frac{4}{3}[/tex]
Then one dress takes [tex]\frac{4}{3}[/tex] of an hour, and the time for twelve dresses is:
[tex]t = 12 \times \frac{4}{3} = 4(4) = 16[/tex]
It would take them 16 hours to sew 12 dresses.
To learn more about the together rate, you can take a look at https://brainly.com/question/25159431
