If it takes 15 hours for 9 people to complete a job, how many hours will it take 12 people

To solve this, we can use the concept of **work-rate**. The number of people and the time taken to complete the job are inversely proportional: as the number of people increases, the time decreases.

We can use the formula:

\[
\text{Work rate} = \frac{\text{Total work}}{\text{Number of people} \times \text{Time taken}}
\]

1. For the initial scenario with 9 people working for 15 hours:
   \[
   \text{Total work} = 9 \times 15 = 135 \text{ person-hours}
   \]

2. Now, we want to know how long it will take 12 people to complete the same job:
   \[
   \text{Time} = \frac{\text{Total work}}{\text{Number of people}}
   \]
   \[
   \text{Time} = \frac{135}{12} = 11.25 \text{ hours}
   \]

Thus, it will take **12 people 11.25 hours** to complete the job.

Would you like further clarification or details? Here are some related questions to explore further:

1. How would the time change if 6 people were working instead of 12?
2. What if the job was split between two teams of different sizes? How would the time be calculated?
3. How would this calculation change if one of the workers left after half the job was done?
4. If the workers' efficiency varied, how would that impact the calculation?
5. What if the total work needed to be doubled? How long would it take 12 people?

**Tip**: When dealing with work-rate problems, remember that more people or higher rates will reduce the time proportionally!

If it takes 15 hours for 9 people to complete a job, how many hours will it take 12 people?

Learn how to calculate the time it takes for 12 people to complete a job that took 9 people 15 hours. This work-rate problem uses inverse proportionality and provides a step-by-step solution. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation