To determine how long it will take for you to be 9 meters away from your neighbor, we can start with the current distance between you and your neighbor, which is 10 meters.
You're moving away from each other at a rate of 5 cm per year, which is equivalent to 0.05 meters per year.
You want the distance between you to become 9 meters. This means you need to decrease the distance by 1 meter (from 10 meters to 9 meters).
To find out how long it will take to decrease the distance by 1 meter given that you are moving apart at a rate of 0.05 meters per year, we can use the formula:
\[ \text{Time (years)} = \frac{\text{Distance change (meters)}}{\text{Rate (meters per year)}} \]
In this case:
\[ \text{Time} = \frac{1 \text{ meter}}{0.05 \text{ meters per year}} = 20 \text{ years} \]
Therefore, it will take 20 years for you to be 9 meters away from your neighbor.