Along the route of a bicycle race, $7$ water stations are evenly spaced between the start and finish lines,
as shown in the figure below. There are also $2$ repair stations evenly spaced between the start and
finish lines. The $3$rd water station is located $2$ miles after the $1$st repair station. How long is the race
in miles?

$\textbf{(A)}\ 8 \qquad \textbf{(B)}\ 16 \qquad \textbf{(C)}\ 24 \qquad \textbf{(D)}\ 48 \qquad \textbf{(E)}\ 96$
Suppose that the race is $d$ miles long. The water stations are located at \[\frac{d}{8}, \frac{2d}{8}, \ldots, \frac{7d}{8}\] miles from the start, and the repair stations are located at \[\frac{d}{3}, \frac{2d}{3}\] miles from the start.
We are given that $\frac{3d}{8}=\frac{d}{3}+2,$ from which  
\begin{align*} \frac{9d}{24}&=\frac{8d}{24}+2 \\ \frac{d}{24}&=2 \\ d&=\boxed{\textbf{(D)}\ 48}. \end{align*}
~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, MRENTHUSIASM