3. (20 points) From village $A$ to village $B$, the Indians take three times as long to travel by canoe as from village $B$ to village $A$. How many times longer than usual can the Indians take to travel from $B$ to $A$ by canoe without paddles?
Answer: 3 times.

Solution: It is not hard to see that village V is upstream from village A. Let's denote the speed of the river current as $v_{r}$, and the average speed of the canoe in still water as $v$. If $S$ is the distance along the river from A to V, then from the condition we have

$$
3 \frac{S}{v+v_{r}}=\frac{S}{v-v_{r}}
$$

From this, we get that

$$
v=2 v_{r}
$$

Let the time it takes for the Indians to travel from V to A without paddles (i.e., only by the river current) be $k$ times longer than with paddles. This gives us the equation

$$
k \frac{S}{v+v_{r}}=\frac{S}{v_{r}}
$$

Then, taking into account $(*)$, we find that $k=3$.