Let \( n \) be the total number of minutes in the documentary. Since they watched one-fourth of the eight-episode documentary and 70 minutes correspond to that one-fourth, we can set up the equation:
\[ \frac{1}{4}n = 70 \]
To find \( n \), we can multiply both sides of the equation by 4:
\[ n = 70 \times 4 \]
Calculating that gives:
\[ n = 280 \]
Thus, the total number of minutes in the documentary is \( \boxed{280} \).