AMC 8 2014 Problem 17

George walks $1$ mile to school. He leaves home at the same time each day, walks at a steady speed of $3$ miles per hour, and arrives just as school begins. Today he was distracted by the pleasant weather and walked the first $\frac{1}{2}$ mile at a speed of only $2$ miles per hour. At how many miles per hour must George run the last $\frac{1}{2}$ mile in order to arrive just as school begins today? $\textbf{(A) }4 \textbf{(B) }6 \textbf{(C) }8 \textbf{(D) }10 \textbf{(E) }12$