To find out how many meters a kudzu vine will grow in 3 weeks, we first need to convert weeks into days.
3 weeks is equal to \( 3 \times 7 = 21 \) days.
Next, we know that kudzu grows at a rate of 3 meters every 10 days. We need to determine how many 10-day periods are in 21 days:
\[ \frac{21 \text{ days}}{10 \text{ days/period}} = 2.1 \text{ periods} \]
Now, we can calculate the growth over 2.1 periods:
\[ 3 \text{ meters/period} \times 2.1 \text{ periods} = 6.3 \text{ meters} \]
Thus, in 3 weeks, a kudzu vine will grow approximately 6.3 meters.