A feed of \(100.0 \mathrm{kmol} / \mathrm{h}\) that is \(60.0 \mathrm{~mol} \%\) methanol, and \(40.0 \mathrm{~mol} \%\) water is sent to a system of three flash drums operating at 1.0 atmosphere. The feed is sent to drum A with \((\mathrm{V} / \mathrm{F})_{\mathrm{A}}=0.666\). After partial condensation, the vapor product from drum \(A\) is the feed to drum \(B\), which operates at \((V / F)_{B}=V_{B} / V_{A}=0.40\). The liquid from drum \(\mathrm{A}\) is partially vaporized and is sent to drum \(\mathrm{C}\). The liquid product from drum \(\mathrm{C}\) is \(15.0 \mathrm{~mol} \%\) methanol. Find flow rates of \(\mathrm{L}_{\mathrm{A}}, \mathrm{L}_{\mathrm{B}}, \mathrm{L}_{\mathrm{C}}, \mathrm{V}_{\mathrm{A}}\), \(\mathrm{V}_{\mathrm{B}}\), and \(\mathrm{V}_{\mathrm{C}}\), and find all unknown vapor and liquid mole fractions.