An article exploring the impact of consumer culture and the psychological effects of excessive material possessions.

The problem presented in the image is a classic example of a work-rate problem, where we need to determine how long it takes for a certain number of workers (in this case, students) to complete a task. Let's break it down step by step.

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Problem Statement:

- A teacher has 10 students who can clean up the classroom in 2 hours.
- The teacher wants to know how many students are needed to clean up the classroom in 45 minutes.

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Solution Approach:

#### Step 1: Understand the work rate of one student.
- If 10 students can clean the classroom in 2 hours, then the total work done (cleaning the classroom) can be represented as 1 job.
- The combined work rate of 10 students is:
\[
\text{Combined work rate of 10 students} = \frac{1 \text{ job}}{2 \text{ hours}}
\]
- Therefore, the work rate of one student is:
\[
\text{Work rate of 1 student} = \frac{1 \text{ job}}{2 \text{ hours}} \div 10 = \frac{1}{20} \text{ jobs per hour}
\]

#### Step 2: Determine the total work required.
- The total work required to clean the classroom is 1 job (as defined earlier).

#### Step 3: Calculate the time constraint.
- The teacher wants the classroom cleaned in 45 minutes. Convert this time into hours:
\[
45 \text{ minutes} = \frac{45}{60} \text{ hours} = \frac{3}{4} \text{ hours}
\]

#### Step 4: Set up the equation for the number of students needed.
- Let \( n \) be the number of students required to clean the classroom in \( \frac{3}{4} \) hours.
- The combined work rate of \( n \) students is:
\[
\text{Combined work rate of } n \text{ students} = n \times \frac{1}{20} \text{ jobs per hour}
\]
- The total work done by \( n \) students in \( \frac{3}{4} \) hours is:
\[
\text{Total work} = \left( n \times \frac{1}{20} \right) \times \frac{3}{4} \text{ hours}
\]
- Since the total work required is 1 job, we set up the equation:
\[
\left( n \times \frac{1}{20} \right) \times \frac{3}{4} = 1
\]

#### Step 5: Solve for \( n \).
- Simplify the equation:
\[
n \times \frac{1}{20} \times \frac{3}{4} = 1
\]
\[
n \times \frac{3}{80} = 1
\]
- Solve for \( n \):
\[
n = \frac{1}{\frac{3}{80}} = \frac{80}{3}
\]
\[
n \approx 26.67
\]

#### Step 6: Interpret the result.
- Since the number of students must be a whole number, we round up to the nearest whole number because partial students cannot perform the task.
- Therefore, the teacher needs 27 students to clean the classroom in 45 minutes.

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Final Answer:

\[
\boxed{27}
\]

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Explanation:

The key to solving this problem is understanding the relationship between the number of workers, their individual work rates, and the total time available. By breaking down the problem into manageable steps and using the concept of work rates, we can determine how many students are needed to complete the task within the given time frame.