jmc

To calculate the average speed, simply evaluate the total distance over the total time. Let the number of additional miles he has to drive be $x.$ Therefore, the total distance is $15+x$ and the total time (in hours) is $$\frac{15}{30}+\frac{x}{55}=\frac{1}{2}+\frac{x}{55}.$$ We can set up the following equation: $$\frac{15+x}{\frac{1}{2}+\frac{x}{55}}=50.$$ Simplifying the equation, we get $$15+x=25+\frac{10x}{11}.$$ Solving the equation yields $x=110,$ so our answer is $\boxed{110}$.