8. A batch of goods is transported from city $A$ to city $B$ by 17 freight trains at a uniform speed of $v$ kilometers per hour. The railway line between $A$ and $B$ is 400 kilometers long. For safety, the distance between two freight trains must not be less than $\left(\frac{v}{20}\right)^{2}$ kilometers. If the length of the freight trains is negligible, then from the departure of the first train, the fastest time required to transport all the goods to city $B$ is $\qquad$ hours.
8. 8. Time $t=\frac{1}{v}\left[400+16 \cdot\left(\frac{v}{20}\right)^{2}\right]=\frac{400}{v}+\frac{v}{25} \geqslant 8$.