A countercurrent extractor with $3$ equilibrium stages is to be used to extract acetic acid from its aqueous solution using isopropyl ether. Equilibrium data for this ternary system is given on ODTUClass and in Table $13-5$ of Wankat. The feed contains $40$ wt$\%$ acetic acid and the balance water and has a flowrate of $2000$ kg$/$h$.$ The solvent used contains $1$ wt$\%$ acetic acid but no water. A raffinate that has $5$ wt$\%$ acetic acid is desired. a$.$ What solvent flowrate is needed? b$.$ What will be the flowrates of the exiting extract and raffinate streams?