Final answer:
It will take Yu Jie, Mufeed, and Mya approximately 6 days to complete a quilt when working together.
Step-by-step explanation:
In order to determine how long it will take the three of them to complete a quilt, we need to calculate their individual rates of work. Yu Jie can complete a quilt in 16 days, Mufeed can complete a quilt in 12 days, and Mya can complete a quilt in 14 days. We can calculate their rates of work by taking the reciprocal of the number of days it takes them to complete a quilt.
Yu Jie's rate of work is 1/16 quilts per day, Mufeed's rate of work is 1/12 quilts per day, and Mya's rate of work is 1/14 quilts per day. To determine how long it will take the three of them to complete a quilt when working together, we add up their rates of work:
1/16 + 1/12 + 1/14 = 105/672 quilts per day.
Since we want to find out how long it will take for them to complete 1 quilt, we take the reciprocal of their combined rate:
672/105 = 6.4 days.
Rounding to the nearest whole day, it will take the three of them approximately 6 days to complete a quilt.