6. A bicycle tire, if installed on the front wheel, will wear out after the bicycle has traveled $5000 \mathrm{~km}$; if installed on the rear wheel, it will wear out after the bicycle has traveled $3000 \mathrm{~km}$. After traveling a certain distance, the front and rear tires can be swapped. If the front and rear tires are swapped, to make a pair of new tires on a bicycle wear out simultaneously, then the bicycle will be able to travel $\qquad$ $\mathrm{km}$.
II. 6.3750.
Let the total wear of each new tire when it is scrapped be $k$. Then the wear per $1 \mathrm{~km}$ for a tire installed on the front wheel is $\frac{k}{5000}$, and the wear per $1 \mathrm{~km}$ for a tire installed on the rear wheel is $\frac{k}{3000}$. Suppose a pair of new tires travels $x \mathrm{~km}$ before the positions are swapped, and $y \mathrm{~km}$ after the positions are swapped. By setting up equations based on the total wear of a tire, we have
$$
\left\{\begin{array}{l}
\frac{k x}{5000}+\frac{k y}{3000}=k, \\
\frac{k y}{5000}+\frac{k x}{3000}=k .
\end{array}\right.
$$

Adding the two equations gives
$$
\frac{k(x+y)}{5000}+\frac{k(x+y)}{3000}=2 k \text {. }
$$

Thus, $x+y=\frac{2}{\frac{1}{5000}+\frac{1}{3000}}=3750$.