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?

Question

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.