To determine how long it will take for Wyatt to catch up to Kirk, we first need to set up the situation in terms of their distances and rates.
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Rates of Swimming:
- Kirk's speed: 3 kilometers per hour
- Wyatt's speed: 3.8 kilometers per hour
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Initial Distance:
- When Wyatt starts swimming, Kirk has already covered 0.2 kilometers.
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Relative Speed: To find out how fast Wyatt is gaining on Kirk, we subtract Kirk's speed from Wyatt's speed: \[ \text{Relative speed} = \text{Wyatt's speed} - \text{Kirk's speed} = 3.8 , \text{km/h} - 3 , \text{km/h} = 0.8 , \text{km/h}. \]
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Distance to Catch Up: The distance that Wyatt needs to cover to catch up to Kirk is the initial distance that Kirk has ahead of Wyatt, which is 0.2 kilometers.
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Time to Catch Up: We then use the formula for time, which is given by: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}}. \] Plugging in the values we have: \[ \text{Time} = \frac{0.2 , \text{km}}{0.8 , \text{km/h}} = \frac{0.2}{0.8} , \text{hours}. \]
Now we simplify the fraction: \[ \frac{0.2}{0.8} = \frac{2}{8} = \frac{1}{4}. \]
Therefore, the time it will take for Wyatt to catch up to Kirk is: \[ \boxed{\frac{1}{4}} \text{ hours} \text{ or } 15 \text{ minutes.} \]