2003 Cayley Problem 20

A car uses 8.4 litres of gas for every 100 km it is driven. A mechanic is able to modify the car's engine at a cost of \$400 so that it will only use 6.3 litres of gas per 100 km. The owner determines the minimum distance that she would have to drive to recover the cost of the modifications. If gas costs \$0.80 per litre, this distance, in kilometres, is between

\textbf{(A)}\ 10\,000 \text{ and } 14\,000\quad \textbf{(B)}\ 14\,000 \text{ and } 18\,000\quad \textbf{(C)}\ 18\,000 \text{ and } 22\,000\quad \textbf{(D)}\ 22\,000 \text{ and } 26\,000\quad \textbf{(E)}\ 26\,000 \text{ and } 30\,000

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.