The area of a rectangular region is increasing at a rate of 250 square feet per hour. Which of the...

1. TRANSLATE the problem information

• Given information:
  • Rate: \(250\) square feet per hour
  • Conversion factor: \(1\) meter \(= 3.28\) feet
  • Target: rate in square meters per minute

2. INFER the conversion strategy

• Since we're dealing with area units, we need to square the linear conversion factor
• We also need to convert time units from hours to minutes
• Dimensional analysis will help us organize the conversions

3. Convert linear units to area units

• If \(1\) meter \(= 3.28\) feet, then:
• \(1\) square meter \(= (3.28 \text{ feet})^2 = 10.7584\) square feet (use calculator)

4. TRANSLATE into dimensional analysis setup

• Set up the conversion chain:

\(250 \frac{\text{sq ft}}{\text{hr}} \times \frac{1 \text{ sq m}}{10.7584 \text{ sq ft}} \times \frac{1 \text{ hr}}{60 \text{ min}}\)

5. SIMPLIFY the calculation

• Multiply the numerators: \(250 \times 1 \times 1 = 250\)
• Multiply the denominators: \(1 \times 10.7584 \times 60 = 645.504\)
• Result: \(\frac{250}{645.504} = 0.3873\) sq m/min (use calculator)

6. Select closest answer choice

• \(0.3873\) is closest to \(0.39\)

Answer: A. 0.39

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students use \(3.28\) directly instead of squaring it for area conversion

Students often think: "\(1\) meter \(= 3.28\) feet, so \(1\) square meter \(= 3.28\) square feet." This fundamental misunderstanding of how area units scale leads to using the wrong conversion factor throughout the problem.

This may lead them to calculate \(\frac{250}{3.28 \times 60} \approx 1.27\), causing them to select Choice B (1.27).

Second Most Common Error:

Poor dimensional analysis execution: Students set up the conversion incorrectly or flip conversion factors

Students might write: \(250 \times \frac{10.7584}{1} \times \frac{60}{1}\) instead of using reciprocals properly, or forget to convert hours to minutes entirely.

This leads to confusion and guessing among the remaining choices.

The Bottom Line:

The key challenge is recognizing that area conversions require squaring the linear conversion factor. Students comfortable with simple unit conversions often miss this crucial step when dealing with derived units like area.