$($a$)$ An ethanol mixture $(96wt.\%$ ethanol, $4wt.\%$water $)$ is a fed to a distillation column together with a pure benzene stream in order to produce pure ethanol. A distillate consisting of $20\mathrm{.}7wt.\%$ ethanol, $6\mathrm{.}6wt.\%$ water and $72\mathrm{.}7wt.\%$ benzene is taken off the top of the column. The bottom stream consists of pure ethanol. Determine how much benzene and ethanol mixture must be fed to produce $750kg{h}^{-1}$ of pure ethanol.