Question

Renee can sew a 25 square-foot quilt in 16 hours. Gerena can sew the same size quilt in 12 hours. How long will it take them to sew the quilt working together?

Answer 1

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
`(1)/(16)t`. the part of the quilt that Gerena sews is
`(1)/(12)t`

Together, they sew one quilt, so

`(1)/(16)t + (1)/(12)t = 1`

Multiply all the terms by 48 (the Least Common Multiple of 16 and 12).

`48\left((1)/(16)t\right)+48\left((1)/(12)t\right) = 48 \\ 3t+4t=48 \\ 7t=48 \\ t=(48)/(7)` hours.