Consider that $1000$ kg of algae slurry is going to be dried from an initial TS content of $10\%$ to a final TS content of $80\%.$ Assuming that the algae slurry is spread to a height of $0\mathrm{.}4$ cm on a black surface that can receive $350$ cal$/($cm$2$d$)$ of radiation. How long $($in hours$)$ does it take to dry the algae slurry to the solid content of $80\%?$ Assume that the density of algae slurry is $1000$ kg$/$m$3.$

$($Please provide the answer in two decimal places$)$