To determine how long it will take for yt and kb to be 10 meters apart, we first need to calculate their current distance apart and the rate at which they are moving away from each other.
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Current Distance:
- The current distance is 7 meters.
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Rate of Movement:
- yt is moving north at a rate of 2.5 cm/year.
- kb is moving south at a rate of 2.5 cm/year.
Therefore, the combined rate at which they are moving away from each other is: \[ 2.5 , \text{cm/year} + 2.5 , \text{cm/year} = 5 , \text{cm/year} \]
Converting this to meters for consistency: \[ 5 , \text{cm/year} = 0.05 , \text{m/year} \]
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Time to Reach 10 Meters Apart:
- They need to go from 7 meters to 10 meters apart, which means they need to increase their distance by: \[ 10 , \text{m} - 7 , \text{m} = 3 , \text{m} \]
Using the rate at which they are moving apart: \[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{3 , \text{m}}{0.05 , \text{m/year}} = 60 , \text{years} \]
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Distance Between Them in 2045:
- Let's assume the current year is 2023. The time from 2023 to 2045 is 22 years.
- The distance they will move apart in that time is: \[ \text{Distance} = \text{Rate} \times \text{Time} = 0.05 , \text{m/year} \times 22 , \text{years} = 1.1 , \text{m} \]
So the distance in 2045 will be: \[ 7 , \text{m} + 1.1 , \text{m} = 8.1 , \text{m} \]
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Distance Between Them in 12 Years' Time:
- In 12 years, they will move apart by: \[ \text{Distance} = 0.05 , \text{m/year} \times 12 , \text{years} = 0.6 , \text{m} \]
So the distance in 12 years will be: \[ 7 , \text{m} + 0.6 , \text{m} = 7.6 , \text{m} \]
Summary of Results:
- Time to be 10 meters apart: 60 years
- Distance in 2045: 8.1 meters
- Distance in 12 years: 7.6 meters