$22.$ Ice has formed on a shallow pond, and a steady state has been reached, with the air above the ice at $-5\mathrm{.}0$C and the bottom of the pond at $4\mathrm{.}0$C$.$ If the total depth of ice $+$ water is $2\mathrm{.}0$ m$,$ how thick is the ice? $($Assume that the thermal conductivities of ice and water are $0\mathrm{.}40$ and $0\mathrm{.}12$ cal$/$m$*$

$$C$*$s$,$ respectively.$)$