Answer :
Let A be the number of days that Andrew uses to paint the house, and B be the number of days that Bailey uses to paint the house. Since Andrew can paint the house 5 times as fast as Bailey and together take 8 days, we can set the following system of equations:
[tex]\begin{gathered} B=5A, \\ \frac{8}{A}+\frac{8}{B}=1. \end{gathered}[/tex]Substituting the first equation in the second one we get:
[tex]\frac{8}{A}+\frac{8}{5A}=1.[/tex]Multiplying the above result by A we get:
[tex]\begin{gathered} (\frac{8}{A}+\frac{8}{5A})\times A=1\times A,_{} \\ 8+\frac{8}{5}=A\text{.} \end{gathered}[/tex]Simplifying the above result we get that:
[tex]A=9\frac{3}{5}.[/tex]Finally, substituting A=9.6 in B=5A we get:
[tex]\begin{gathered} B=5\cdot9\frac{3}{5}, \\ B=48. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} \text{Andrew: 9}\frac{3}{5}\text{ days,} \\ \text{Bailey: 48 days.} \end{gathered}[/tex]