$(55)3.$ The Swiss Water Process $($SWP$)$ offers an organic$-$solvent$-$free method for decaffeinating unroasted, green coffee beans. Green coffee beans consist of approximately $80\%$ insoluble solids, $18\mathrm{.}8\%$ soluble flavor compounds, and $1\mathrm{.}2\%$ caffeine on a mass basis. In the Swiss Water Process, coffee beans $($Stream $1)$ are soaked in hot flavored water $($a caffeine$-$free coffee extract that contains only water and flavor$)($Stream $2).$ This extraction removes essentially all of the caffeine to produce decaffeinated beans $($Stream $3)$ with a moisture content of $7\mathrm{.}0\%$ by weight. The water leaving the extractor $($Stream $4)$ carries both caffeine $(5\mathrm{.}0wt\%)$ and flavor compounds. It undergoes filtration using activated charcoal to isolate and capture all of the caffeine $($Stream $5),$ while leaving all of the flavor compounds in the water. After filtration, the water is ready again to extract caffeine from more coffee beans and is recycled. Additional water $($Stream $7)$ is added to the recycle loop $($Stream $6)$ to maintain a steady flowrate of the flavored water $($Stream $2)$ through the extractor. By recycling the flavored water it becomes saturated with flavor compounds so that these flavors are not removed, but are retained by the coffee beans. The caffeinated flavored water leaving the extraction vessel $($Stream $4)$ has a flavor$-$to$-$water ratio of $2\mathrm{.}0kg$ of flavor per $125kg$ of water.

a$)$ What is the mass flowrate of flavors in the decaffeinated beans $($stream $3)?$

b$)$ How much pure water $($stream $7)$ is required $($in $k\frac{g}{h})?$

c$)$ What is the mass flowrate of flavored water $($stream $2)$ entering the extractor?

d$)$ What is the mass fraction of flavors in stream $4?$