Two boats race across a $70$ km lake and back. The first boat travels at a constant $63\mathrm{.}0$ km$/$h across the lake and back. The second boat travels at $31\mathrm{.}0$ km$/$h across the lake, and $95\mathrm{.}0$ km$/$h back. By what distance $($in km$)$ did the winner beat the loser?