Qiang drives $15$ miles at an average speed of $30$ miles per hour. How many additional miles will he have to drive at $55$ miles per hour to average $50$ miles per hour for the entire trip?
$\textbf{(A) }45\qquad\textbf{(B) }62\qquad\textbf{(C) }90\qquad\textbf{(D) }110\qquad\textbf{(E) }135$
The only option that is easily divisible by $55$ is $110$, which gives 2 hours of travel. And, the formula is $\frac{15}{30} + \frac{110}{55} = \frac{5}{2}$.
And, $\text{Average Speed}$ = $\frac{\text{Total Distance}}{\text{Total Time}}$.
Thus, $\frac{125}{50} = \frac{5}{2}$.
Both are equal and thus our answer is $\boxed{\textbf{(D)}\ 110}.$