A bar of aluminum is contaminated with copper at a concentration three times the acceptable limit$.$ It is to be purified by directional solidification, with a planar growth front. Estimate the fraction of the bar that will have an acceptable purity.

Given: $T_m(Al)=660C,T_E=548C,x_{\text{m}\text{a}\text{x}}=5\mathrm{.}65wt\%,$ and $x_{\text{E}\text{u}\text{t}\text{e}\text{c}\text{t}\text{i}\text{c}}=33\mathrm{.}2$ wt $\%Cu.$