A preheater and a distillation column are maintained by engineers Marcella and Julius. A stream of pure acetone $(A,C_3{H}_{6}O)$ and a stream containing acetone, ethanol $(E,C_2{H}_{5}OH),$ and butanol $(B,C_4{H}_{9}OH)$ enter the preheater. One stream exits the preheater containing $114mo\frac{l}{m}in$ butanol, some acetone, and some ethanol; the mole fractions of butanol and ethanol are $0\mathrm{.}209$ and $0\mathrm{.}412,$ respectively. The stream of pure acetone entering the preheater is $2\mathrm{.}02$ times larger than the component flow rate of acetone in the other stream entering the preheater. The stream exiting the preheater enters a distillation column, and all of the entering butanol exits in the bottom product stream. The recoveries in the overhead product, which is defined and the ratio of component flow rate exiting to component flow rate entering the distillation column, of acetone and ethanol are $83\mathrm{.}1\%$ and $59\mathrm{.}2\%,$ respectively. Determine the following three unknowns.

Component flow rate of pure acetone entering the preheater $=mo\frac{l}{m}in$

Component flow rate of ethanol exiting in the bottom product of the distillation column $=mo\frac{l}{m}in$

Component flow rate of acetone exiting in the overhead product of the distillation column $=mo\frac{l}{m}in$