A feed stream to a distillation column, flowing at a rate of $1200k\frac{g}{h},$ contains a gas mixture of ethanol, methanol, and propanol. The feed contains $20wt\%$ methanol. The distillate consists of $90\%$ of the methanol and $60\%$ of the ethanol contained in the feed. All of the $400k\frac{g}{h}$ of propanol fed to the process ends up in the bottom of the column. Calculate the bottom stream mass flow rate.