A solid is dried at constant drying conditions from $0\mathrm{.}70$ to $0\mathrm{.}50$ g moisture per g dry solid in $3$ hours. The rate of drying during the falling rate period is second order with respect to the moisture content. Determine the time needed to dry the solid from the critical moisture content of $0\mathrm{.}50$ to $0\mathrm{.}30$ g moisture per g dry solid.