Let \( t \) be the time in hours that Sam and Keith will be traveling until they are the same distance from their campsite.
For Sam:
- Initial distance from the campsite: 21 km
- Speed of Sam's boat: 27 km/h
- Distance traveled by Sam after \( t \) hours: \( 27t \)
- Distance from the campsite after \( t \) hours: \[ 21 - 27t \]
For Keith:
- Initial distance from the campsite: 7 km
- Speed of Keith's paddleboard: 6 km/h
- Distance traveled by Keith after \( t \) hours: \( 6t \)
- Distance from the campsite after \( t \) hours: \[ 7 - 6t \]
Now, we need to find \( t \) when their distances from the campsite are equal: \[ 21 - 27t = 7 - 6t \]
Next, we'll solve for \( t \):
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Rearranging the equation: \[ 21 - 7 = 27t - 6t \] simplifies to: \[ 14 = 21t \]
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Solving for \( t \): \[ t = \frac{14}{21} = \frac{2}{3} \text{ hours} \]
Thus, it will take them \( \frac{2}{3} \) hours or \( 40 \) minutes to be the same distance from their campsite.