Answer: Time taken by Ximena to paint the fence alone  = 24 hours
Time taken by Candice to paint the fence alone = 12 hours
Step-by-step explanation:
Let x= Time taken by Ximena to paint the fence alone .
Time taken by Candice to paint the fence alone = x-12
As per given , we have
[tex]\dfrac{1}{x}+\dfrac{1}{x-12}=\dfrac{1}{8}\\\\\Rightarrow\ \dfrac{x-12+x}{x(x-12)}=\dfrac{1}{8}\\\\\Rightarrow\ 8(2x-12)=x^2-12x\\\\\Rightarrow\ 16x-96=x^2-12x\\\\\Rightarrow\ x^2-12x-16x+96=0\\\\\Rightarrow\ x^2-28x+96=0\\\\\Rightarrow\ x^2-4x-24x+96=0\\\\\Rightarrow\ x(x-4)-24(x-4)=0\\\\\Rightarrow\ (x-4)(x-24)=0\\\\\Rightarrow x=4, 24[/tex]
if x= 4
Time taken by Ximena = 4 hours
Time taken by Candice = 4-12 hours =-8 hours which is not possible. (time cannot be negative)
Therefore, x= 24
Such that
Time taken by Ximena to paint the fence alone  = 24 hours
Time taken by Candice to paint the fence alone = 24-12=12 hours
