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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? (2014 AMC 10A Problems, Question \#15) 
Overseas Competition->Knowledge Point->Calculation Modules
Note that he drives at $50$ miles per hour after the first hour and continues doing so until he arrives. Let $d$ be the distance still needed to travel after $1$ hour. We have that $\frac{d}{50}+1.5=\frac{d}{35}$, where the $1.5$ comes from $1$ hour late decreased to $0.5$ hours early. Simplifying gives $7 d+525=10 d$, or $d=175$. Now, we must add an extra $35$ miles traveled in the first hour, giving a total of (C) $210$ miles. 