Answer: [tex]6\dfrac{6}{7}\text{ hours}[/tex]
Step-by-step explanation:
We know that if A takes time x and B time y to do a job individually, then the total time taken both of them if they work together is given by :-
[tex]\dfrac{1}{T}=\dfrac{1}{x}+\dfrac{1}{y}[/tex]
According to the given question, substitute x= 16 and y= 12 in the above equation, we get the total time taken to sew the quilt working together is given by :-
[tex]\dfrac{1}{T}=\dfrac{1}{16}+\dfrac{1}{12}\\\\Rightarrow\\dfrac{1}{T}=\dfrac{7}{48}\\\\\Rightarrow\ T=\dfrac{48}{7}=6\dfrac{6}{7}[/tex]
Hence, the time taken to sew the quilt working together = [tex]6\dfrac{6}{7}\text{ hours}[/tex]
