Let v (mph), t(h), a(mi) be Bob's speed, the time Bob traveled and the answer

\(\left\{{}\begin{matrix}\left(v+5\right)\left(t+1\right)=vt+50\\\left(v+10\right)\left(t+2\right)=vt+a\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}vt+v+5t+5=vt+50\\vt+2v+10t+20=vt+a\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}v+5t=45\\2v+10t=a-20\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2v+10t=90\\2v+10t=a-20\end{matrix}\right.\)\(\Rightarrow a=110\)

So, the answer is 110 miles