To determine how long it will take for Sam and Keith to be the same distance from their campsite, we can set up equations based on their speeds and distances.
Let's denote:
- \( t \) as the time in hours until they are the same distance from the campsite.
For Sam:
- Initial distance from the campsite: 21 kilometers
- Speed: 27 kilometers per hour
After \( t \) hours, Sam's distance from the campsite will be: \[ \text{Distance}_{Sam} = 21 - 27t \]
For Keith:
- Initial distance from the campsite: 7 kilometers
- Speed: 6 kilometers per hour
After \( t \) hours, Keith's distance from the campsite will be: \[ \text{Distance}_{Keith} = 7 - 6t \]
Set the distances equal:
To find when they are the same distance from the campsite, we set the equations equal to each other: \[ 21 - 27t = 7 - 6t \]
Solve for \( t \):
- Rearranging the equation: \[ 21 - 7 = 27t - 6t \] simplifies to: \[ 14 = 21t \]
- Divide both sides by 21: \[ t = \frac{14}{21} = \frac{2}{3} \text{ hours} \]
Conclusion:
It will take \( \frac{2}{3} \) hours, which is 40 minutes, for Sam and Keith to be the same distance from their campsite.