3. From Nizhny Novgorod to Astrakhan, a steamboat takes 5 days, and on the return trip - 7 days. How long will it take for rafts to float from Nizhny Novgorod to Astrakhan?
3. When the steamboat goes from Nizhny Novgorod to Astrakhan (downstream), it covers $\frac{1}{5}$ of the distance in a day, and when it goes back - $\frac{1}{7}$ of the distance. Therefore, $\frac{1}{5}-\frac{1}{7}=\frac{2}{35}$ - two current speeds. From this, $\frac{1}{35}$ of the distance per day is the speed of the current. Consequently, rafts will take 35 days to float from Nizhny to Astrakhan.