\(\left\{{}\begin{matrix}s=\dfrac{1}{2}gt^2\\s'=\dfrac{1}{2}g\left(t-1\right)^2\end{matrix}\right.\)
\(\Delta s=s-s'=45\)
\(\Leftrightarrow\dfrac{1}{2}gt^2-\dfrac{1}{2}g\left(t-1\right)^2=45\)
\(\Leftrightarrow g\left(t-\dfrac{1}{2}\right)=45\)
\(\Rightarrow t=5s\)