The ages of two sisters are 11 and 8 years. In how many years time will the product of their ages be 208?

Answer 1

Let the number of years be $x$. Then, in $x$ years, the ages of the two sisters will be $11+x$ and $8+x$. We have the equation $(11+x)(8+x)=208$, which expands to $x^2+19x-40=0$. Factoring, we get $(x+20)(x-1)=0$, so either $x=-20$ or $x=1$. Since time cannot be negative, the answer is $\boxed{1}$ year.