$11\mathrm{.}32.$ Potable water containing not more than $500ppm$ dissolved salt is made by desalinization through reverse osmosis of seawater which contains $3\mathrm{.}0\%$ sait. Fresh seawater is admitted at a rate of $1000k\frac{g}{h}.$ Potable water is withdrawn from the reverse osmosis cell as product while a fraction of the brine that leaves the cell and containing $5\mathrm{.}25\%$ salt is recycled. The concentration of salt in the stream entering the cell after mixing the recycle stream with fresh seawater is $4\mathrm{.}0\%.$ Determine:

$($a$)$ The rate at which brine is removed from the plant $(k\frac{g}{h})562\mathrm{.}31k\frac{g}{h}$

$($b$)$ The rate at which potable water is produced $(k\frac{g}{h}),432\mathrm{.}69k\frac{g}{h}$

$($c$)$ The fraction of the brine leaving the cell that is recycled. $0\mathrm{.}5851$