This kind of problem assumes that the two people working together work for the same amount of time.
Renee can sew a quilt in 16 hours, so she can sew 1/16 of a quilt each hour. Gerena sews a quilt in 12 hours, so she can sew 1/12 of a quilt each hour.
Use the variable t represent the time Renee and Gerena work together (measured in hours). The part of a quilt Renee sews is [tex] \frac{1}{16}t [/tex]. the part of the quilt that Gerena sews is [tex] \frac{1}{12}t [/tex]
Together, they sew one quilt, so
[tex] \frac{1}{16}t + \frac{1}{12}t = 1 [/tex]
Multiply all the terms by 48 (the Least Common Multiple of 16 and 12).
[tex] 48\left(\frac{1}{16}t\right)+48\left(\frac{1}{12}t\right) = 48 \\ 3t+4t=48 \\ 7t=48 \\ t=\frac{48}{7} [/tex] hours.
