An object's speed is 64 yards per second. What is the object's speed, in feet per second? (1text{ yard} =...

1. TRANSLATE the problem information

• Given information:
  • Current speed: 64 yards per second
  • Conversion factor: 1 yard = 3 feet
• What we need: Speed in feet per second

2. INFER the conversion strategy

• Since we want to convert from yards to feet, we need to multiply by the conversion factor
• The conversion factor should be set up as: (3 feet/1 yard) so the yard units cancel out

3. SIMPLIFY by performing the calculation

• Speed in feet per second = \(64 \text{ yards/second} \times (3 \text{ feet}/1 \text{ yard})\)
• Speed in feet per second = \(64 \times 3 \text{ feet/second} = 192 \text{ feet/second}\)

Answer: D. 192

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may not understand the proper method for unit conversion and instead add or subtract the conversion factor.

For example, they might think: "To convert to feet, I need to add 3" → \(64 + 3 = 67\), leading them to select Choice B (67)

Or they might think: "Since yards are bigger than feet, I subtract" → \(64 - 3 = 61\), leading them to select Choice A (61)

Second Most Common Error:

Poor INFER reasoning: Students might recognize they need to use multiplication but set up the conversion factor incorrectly (dividing instead of multiplying).

This leads to \(64 \div 3 \approx 21.33\), which doesn't match any answer choice and causes confusion and guessing.

The Bottom Line:

This problem tests whether students understand that unit conversion requires multiplying by conversion factors, not simple arithmetic operations like addition or subtraction. The key insight is that when converting to smaller units (yards to feet), the numerical value should increase.