Question

The amount of time it takes for a crew of people to finish a job varies inversely with the number of people on the crew. If it takes a crew of 3 people 8 hours to complete a job, how long will the same job take a crew of 5 people?

4.8 hours

1.9 hours

9.2 hours

13.3 hours

Answer 1

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 \( k \):

1. Substitute \( T = 8 \) hours and \( N = 3 \) into the equation:

\[ 8 = k \cdot \frac{1}{3} \]

2. 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 \( k \):

3. Substitute \( N = 5 \) into the equation:

\[ T = 24 \cdot \frac{1}{5} \]

4. 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**.