Answer: 6.62 weeks
Step-by-step explanation:
Time taken by Ryan to build a home = 13.4 weeks
Time taken by Jack to build the same home = 13.1 weeks
Let t be the time to complete a house if they work together, then
[tex]\frac{1}{t}=\frac{1}{t}[/tex]= [tex]\frac{1}{\text{time taken by Ryan alone}}+\frac{1}{\text{time taken by Jack alone}}[/tex]
[tex]=\frac{1}{13.4}+\frac{1}{13.1}\\\\=\frac{13.1+13.4}{175.54}\\\\=\frac{26.5}{175.54}[/tex]
[tex]\\\Rightarrow\ t=\frac{175.54}{26.5}\\\Rightarrow\ t=6.62\ weeks[/tex]
