To model the problem, we can use the following equation:
\[ 20s = 200 \]
where \( s \) is the length of each station, and \( 20 \) represents the number of vendors (or stations). The total length they occupy is given as \( 200 \) feet.
Now, we can solve the equation for \( s \):
- Divide both sides of the equation by \( 20 \):
\[ s = \frac{200}{20} \]
- Calculate the division:
\[ s = 10 \]
Thus, each station is \( 10 \) feet long.