A mooring line measures 13 fathoms in length. Given that 1text{ fathom} = 6text{ feet} and 1text{ yard} = 3text{...

1. TRANSLATE the problem information

• Given information:
  • 13 fathoms (what we're converting)
  • 1 fathom = 6 feet
  • 1 yard = 3 feet
  • Need to find: length in yards

2. INFER the conversion strategy

• We need to get from fathoms to yards, but we're not given a direct conversion
• Strategy: Convert fathoms → feet → yards using the given relationships
• Alternative insight: We can find how many yards equal 1 fathom, then multiply

3. SIMPLIFY the stepwise conversion

• First conversion: \(13 \text{ fathoms} \times 6 \text{ feet/fathom} = 78 \text{ feet}\)
• Second conversion: \(78 \text{ feet} \div 3 \text{ feet/yard} = 26 \text{ yards}\)

4. Verify with direct ratio (optional)

• INFER the direct relationship: If \(1 \text{ fathom} = 6 \text{ feet}\) and \(3 \text{ feet} = 1 \text{ yard}\), then \(1 \text{ fathom} = 6/3 = 2 \text{ yards}\)
• SIMPLIFY: \(13 \text{ fathoms} \times 2 \text{ yards/fathom} = 26 \text{ yards}\) ✓

Answer: B (26)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse which direction to multiply or divide in unit conversions, especially when dealing with multiple conversion steps.

They might calculate: \(13 \div 6 \div 3 = 0.72\) or \(13 \times 6 \times 3 = 234\), not understanding that you multiply by one conversion factor and divide by another. This leads to confusion and guessing among the given choices.

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors in the calculations, such as computing \(78 \div 3 = 24\) instead of 26.

This may lead them to select Choice D (24).

The Bottom Line:

Unit conversion problems require careful attention to the direction of conversion factors. The key insight is recognizing whether each step requires multiplication or division based on the units you're converting from and to.