Reverse osmosis $($RO$)$ is being used more widely for treating groundwater for human

consumption. RO treatment can produce water that essentially has no hardness.

Hardness in water is attributed to divalent metallic cations primarily, calcium $(C{a}^{2+})$

and magnesium $(M{g}^{2+}).$ A $3\mathrm{.}785$ mega$-$liter $($ML$)$ RO water treatment plant $($WTP$)$

treats groundwater containing $150m\frac{g}{L}$ of hardness as $CaC{O}_3.$ The product or

permeate from the RO WTP will be blended with untreated groundwater to achieve a

final hardness of $50m\frac{g}{L}$ as $CaC{O}_3.$ How much of the untreated groundwater must

be blended with permeate from the RO WTP$?$ See the schematic diagram below to

assist in the solution of the problem.

Figure E$5\mathrm{.}13$