To find the hours \( t \) after which Jamie's distance from the peak will be 900 feet, we can start by understanding that Jamie is initially climbing a total of 1,500 feet to reach the peak.
At a height of 900 feet from the peak, Jamie will be at a height of \( 1,500 - 900 = 600 \) feet from the base of the mountain.
Using the constant rate of 300 feet/hour, we can set up the equation:
\[ \text{Distance climbed} = 300t \]
To determine the time when Jamie is 600 feet up, we can set the equation:
\[ 300t = 600 \]
Now, we solve for \( t \):
\[ t = \frac{600}{300} = 2 \text{ hours} \]
However, after reaching the peak, he will climb down 900 feet to again be 900 feet from the peak. Since he starts descending right after reaching the peak (at 1,500 feet), the time to descend 600 feet is calculated similarly:
\[ \text{Distance down} = 300t \]
Setting the equation:
\[ 1500 - 300t = 900 \]
Rearranging gives:
\[ 300t = 1500 - 900 = 600 \]
Thus, solving for \( t \):
\[ t = \frac{600}{300} = 2 \text{ hours} \]
So we have two instances:
- Climbing to 600 feet from the base, which takes 2 hours.
- Descending back down to 900 feet from the peak, which takes another 2 hours.
The answer you are looking for is:
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The equation that can be used to find the number of hours, \( t \), after which Jamie's distance from the peak will be 900 feet is:
\( 300t = 600 \)
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Jamie will be 900 feet from the peak after:
2 hours (climbing up)
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And after:
2 hours (descending down from the peak), which would be at a total of \( 2 + 2 = 4 \) hours from start.
So, summarizing:
- The equation: \( 300t = 600 \)
- After: 2 hours
- After: 4 hours (total time from start - 2 hours climbing + 2 hours descending)