The speed of a vehicle is increasing at a rate of 7.3 meters per second squared. What is this rate,...

1. TRANSLATE the problem information

• Given information:
  • Current rate: \(7.3\) meters per second squared
  • Conversion factor: \(1 \text{ mile} = 1,609 \text{ meters}\)
  • Target: miles per minute squared, rounded to nearest tenth

2. INFER the conversion approach

• We need two conversions:
  • Distance: meters → miles
  • Time: seconds² → minutes²
• Key insight: Since we have seconds squared in the denominator, we need to convert seconds² to minutes², not just seconds to minutes

3. Set up the distance conversion factor

• Since \(1 \text{ mile} = 1,609 \text{ meters}\)
• Conversion factor: \(\frac{1 \text{ mile}}{1,609 \text{ meters}}\)

4. INFER the time conversion factor

• Since \(1 \text{ minute} = 60 \text{ seconds}\)
• Then \(1 \text{ minute}^2 = (60 \text{ seconds})^2 = 3,600 \text{ seconds}^2\)
• Conversion factor: \(\frac{3,600 \text{ seconds}^2}{1 \text{ minute}^2}\)

5. TRANSLATE into one calculation

• Complete setup: \(7.3 \text{ meters/second}^2 \times \frac{1 \text{ mile}}{1,609 \text{ meters}} \times \frac{3,600 \text{ seconds}^2}{1 \text{ minute}^2}\)

6. SIMPLIFY the calculation

• \(= 7.3 \times \frac{1}{1,609} \times 3,600 \text{ miles/minute}^2\)
• \(= 7.3 \times \frac{3,600}{1,609} \text{ miles/minute}^2\)
• \(= \frac{26,280}{1,609} \text{ miles/minute}^2\) (use calculator)
• \(\approx 16.33 \text{ miles/minute}^2\)
• Rounded to nearest tenth: \(16.3 \text{ miles/minute}^2\)

Answer: B. 16.3

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students recognize they need to convert seconds to minutes but forget that seconds² requires squaring the conversion factor. They use 60 instead of 3,600.

Their calculation: \(7.3 \times \frac{1}{1,609} \times 60 \approx 0.27\), which rounds to \(0.3\)

This leads them to select Choice A (0.3)

Second Most Common Error:

Poor TRANSLATE reasoning: Students flip the conversion factors, setting up \(7.3 \times \frac{1,609}{1} \times \frac{60}{3,600}\) instead of the correct ratios.

Their calculation: \(7.3 \times 1,609 \times \frac{1}{60} \approx 195.8\)

This leads them to select Choice C (195.8)

The Bottom Line:

The key challenge is recognizing that squared units in the denominator require squaring the time conversion factor. Students who treat "seconds squared" the same as "seconds" will consistently get the wrong answer.