2014 Fermat Problem 16

At the start of a 5 hour trip, the odometer in Jill's car indicates that her car had already been driven 13\,831 km. The integer 13\,831 is a palindrome, because it is the same when read forwards or backwards. At the end of the 5 hour trip, the odometer reading was another palindrome. If Jill never drove faster than 80 km/h, her greatest possible average speed was closest to

\textbf{(A)}\ 62 \text{ km/h}\quad \textbf{(B)}\ 20 \text{ km/h}\quad \textbf{(C)}\ 42 \text{ km/h}\quad \textbf{(D)}\ 16 \text{ km/h}\quad \textbf{(E)}\ 77 \text{ km/h}

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