AMC 12 2014a Problem 11

David drives from his home to the airport to catch a flight. He drives $35$ miles in the first hour, but realizes that he will be $1$ hour late if he continues at this speed. He increases his speed by $15$ miles per hour for the rest of the way to the airport and arrives $30$ minutes early. How many miles is the airport from his home?

$\textbf{(A) }140 \textbf{(B) }175 \textbf{(C) }210 \textbf{(D) }245 \textbf{(E) }280$