A distance of 354 furlongs is equivalent to how many feet? (1 furlong = 220 yards and 1 yard =...

1. TRANSLATE the problem information

• Given information:
  • Distance: 354 furlongs
  • Conversion factors: \(1 \text{ furlong} = 220 \text{ yards}\), \(1 \text{ yard} = 3 \text{ feet}\)
  • Need to find: equivalent distance in feet

2. INFER the conversion strategy

• Since we need to go from furlongs → feet, but we have furlongs → yards → feet
• We need to chain the conversion factors: furlongs → yards → feet
• Set up: \(354 \text{ furlongs} \times \frac{220 \text{ yards}}{1 \text{ furlong}} \times \frac{3 \text{ feet}}{1 \text{ yard}}\)

3. SIMPLIFY through sequential calculations

• First conversion (furlongs to yards): \(354 \times 220 = 77,880 \text{ yards}\) (use calculator)
• Second conversion (yards to feet): \(77,880 \times 3 = 233,640 \text{ feet}\) (use calculator)
• Notice how the units cancel: \(\text{furlongs} \times \frac{\text{yards}}{\text{furlong}} \times \frac{\text{feet}}{\text{yard}} = \text{feet}\)

Answer: 233,640 feet (Choice D)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students correctly set up the conversion but make calculation errors or forget the final step.

For example, they might calculate \(354 \times 220 = 77,880\) yards correctly but then forget to multiply by 3 to convert to feet. This incomplete solution gives them 77,880, but since that's not an option, they might estimate or pick the closest value like Choice C (25,960).

Second Most Common Error:

Poor TRANSLATE reasoning: Students struggle with setting up the conversion factors correctly or try to find shortcuts.

They might attempt to work backwards from the answer choices or guess at direct conversion rates instead of systematically using the given conversion factors. This leads to confusion and random guessing among the available choices.

The Bottom Line:

This problem tests whether students can systematically apply dimensional analysis with multiple conversion steps. The key is methodically setting up the conversion chain and carefully executing each arithmetic step rather than trying shortcuts or skipping steps.