Maximus and Theodora are optimizing a steady state process for maling orange juice concentrate. A stream of oranges $(O)$ and a stream of water $(W,H_{2}O)$ enter a juicing machine. The exit stream from the juicing machine contains $55\mathrm{.}8k\frac{g}{h}r$ orange juice $($OJ$,$ MW $=108),21\mathrm{.}3k\frac{g}{h}r$ pulp solids $($PS$),$ and $37\mathrm{.}5k\frac{g}{h}r$ water. The exit stream from the juicing machine enters a filter. The filter removes all of the pulp solids and $19\mathrm{.}2\%$ of the water entering the filter as one exiting stream. The other stream exiting the filter contains water and orange juice. The water$/$orange juice mixture is finally sent to an evaporator to produce a concentrate stream $(80\mathrm{.}6wt\%$ orange juice and the balance water$)$ and a stream of pure water. The pure water is recycled, mixed with a fresh stream of pure water, and fed into the juicing machine. Determine the following three unknowns.

Mole fraction of orange juice in the concentrate stream $=$

Mass flow rate of water entering the evaporator $=k\frac{g}{h}r$

Mass flow rate of water entering the overall system $=k\frac{g}{h}r$