In isosceles triangle $\triangle abc$ we have $ab=ac=4$. The altitude from $b$ meets $\overline{ac}$ at $h$. If $ah=3(hc)$ then determine $bc$.

At work claire has a deadline that is rapidly approaching. as she works, she finds that she is doing more work in a shorter amount of time than usual. she thinks mor quickly, and her senses and memory are sharper. what is responsible for claire working more effectively?