Let the woman's age be 10x+y. Her husband's age is 10y+x. The equation is $(10y+x)-(10x+y) = (1/11)(11x+11y)$. This simplifies to $9y-9x = x+y$, or $8y=10x$, which means $y/x = 5/4$. The only single digits that fit this ratio are y=5 and x=4. So, the woman's age is 45.