Block $1,$ with mass $m_1$ and speed $3\mathrm{.}4\frac{m}{s},$ slides along an $x$ axis on a frictionless floor and then undergoes a one$-$dimensional elastic collision with stationary block $2,$ with mass $m_2=0\mathrm{.}53m_1.$ The two blocks then slide into a region where the coefficient of kinetic friction is $0\mathrm{.}31$ ; there they stop. How far into that region do $($a$)$ block $1$ and $($b$)$ block $2$ slide?