Let's call [tex]a[/tex] the number of hours it takes for A to fill the pool and [tex]b[/tex] the number of hours it takes for B to fill the pool.
We have [tex]a=b-3[/tex] and [tex]\frac{2}a+\frac{2}b=1[/tex] hence [tex]\frac{2}{b-3}+\frac{2}b=1\Leftrightarrow b^2-7b+6=0\Leftrightarrow b=6\text{ or }b=-1[/tex] hence [tex]b=6[/tex] and thus [tex]a=3[/tex].
[tex]\boxed{b=6,a=3}[/tex]
