An insect moves at a speed of 3/20 feet per second. What is this speed, in yards per second? (3...

1. TRANSLATE the problem information

• Given information:
  • Speed: \(\frac{3}{20}\) feet per second
  • Conversion: \(3\mathrm{\ feet} = 1\mathrm{\ yard}\)
  • Need to find: speed in yards per second

2. INFER the conversion approach

• Since we're converting from feet to yards, we need to multiply by a conversion factor
• The conversion factor must be set up so feet cancel out and we're left with yards
• We'll use: \(\frac{1\mathrm{\ yard}}{3\mathrm{\ feet}}\) so the "feet" units cancel

3. TRANSLATE into dimensional analysis setup

• Set up the multiplication: \(\left(\frac{3}{20}\frac{\mathrm{feet}}{\mathrm{second}}\right) \times \left(\frac{1\mathrm{\ yard}}{3\mathrm{\ feet}}\right)\)
• Notice how "feet" in the numerator and denominator will cancel

4. SIMPLIFY the calculation

• \(\frac{3}{20} \times \frac{1}{3} = \frac{3 \times 1}{20 \times 3} = \frac{3}{60}\)
• Reduce the fraction: \(\frac{3}{60} = \frac{1}{20}\)

Answer: A \(\left(\frac{1}{20}\right)\)

Alternative acceptable forms: \(\frac{1}{20}\), \(0.05\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students set up the conversion factor backwards as \(\frac{3\mathrm{\ feet}}{1\mathrm{\ yard}}\) instead of \(\frac{1\mathrm{\ yard}}{3\mathrm{\ feet}}\).

When they calculate \(\frac{3}{20} \times \frac{3}{1}\), they get \(\frac{3}{20} \times 3 = \frac{9}{20}\).

This leads them to select Choice B \(\left(\frac{9}{20}\right)\).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misunderstand what "conversion" means and think they should multiply \(\frac{3}{20}\) by 3 directly (thinking "3 feet equals 1 yard, so multiply by 3").

This gives them \(\frac{3}{20} \times 3 = \frac{9}{20}\), also leading to Choice B \(\left(\frac{9}{20}\right)\).

The Bottom Line:

The key challenge is understanding that converting from a smaller unit (feet) to a larger unit (yards) requires dividing by the conversion number, which means multiplying by its reciprocal in dimensional analysis.