To solve this problem, we will use the concept of inverse variation. When the amount of time it takes a crew to finish a job varies inversely with the number of people, we can express this relationship mathematically as:
\[ T = k \cdot \frac{1}{N} \]
where:
- \( T \) is the time taken to complete the job,
- \( N \) is the number of people in the crew,
- \( k \) is a constant.
Given that it takes a crew of 3 people 8 hours to complete the job, we can find the constant \( k \):
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Substitute \( T = 8 \) hours and \( N = 3 \) into the equation:
\[ 8 = k \cdot \frac{1}{3} \]
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To find \( k \), multiply both sides by 3:
\[ k = 8 \cdot 3 = 24 \]
Now, we want to find out how long it will take a crew of 5 people to complete the same job. Using the constant \( k \):
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Substitute \( N = 5 \) into the equation:
\[ T = 24 \cdot \frac{1}{5} \]
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Calculate \( T \):
\[ T = \frac{24}{5} = 4.8 \text{ hours} \]
So, the same job will take a crew of 5 people 4.8 hours.
Therefore, the answer is 4.8 hours.
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