A batch distillation column with eight theoretical stages (first stage is the still pot) is charged with \(500 \mathrm{kmol}\) of a \(48.8 \mathrm{~mol} \%\) A in B mixture at atmospheric pressure (relative volatility \(\alpha_{A B}=2.0\) ). The boil-up rate is constant at \(213.5 \mathrm{kmol} / \mathrm{h}\). If the distillate composition is to be maintained constant at \(95 \mathrm{~mol} \%\) A by varying the reflux ratio, calculate the distillation time required to reduce the still composition to \(19.2 \mathrm{~mol} \%\) A. Calculate the fractional recovery of A in the distillate.