AMC 12 2014b Problem 10

Danica drove her new car on a trip for a whole number of hours, averaging 55 miles per hour. At the beginning of the trip, $abc$ miles was displayed on the odometer, where $abc$ is a 3-digit number with $a \geq{1}$ and $a+b+c \leq{7}$. At the end of the trip, the odometer showed $cba$ miles. What is $a^2+b^2+c^2?$.

\textbf{(A)}\ 26 \textbf{(B)}\ 27 \textbf{(C)}\ 36 \textbf{(D)}\ 37 \textbf{(E)}\ 41