A competition consisted of four different events. One participant completed the first event with an average speed of 20.300 miles...

1. TRANSLATE the problem information

• Given information:
  • Speed: \(\mathrm{20.300\ miles\ per\ hour}\)
  • Conversion factor: \(\mathrm{1\ mile = 1,760\ yards}\)
  • Need to find: speed in yards per hour

2. INFER the conversion strategy

• To convert from miles per hour to yards per hour, we need to multiply by the conversion factor
• Set up dimensional analysis: \(\mathrm{(miles/hour) \times (yards/mile) = yards/hour}\)
• The "miles" units will cancel, leaving us with yards/hour

3. SIMPLIFY by performing the calculation

• Speed in yards per hour = \(\mathrm{20.300 \times 1,760}\)
• Using a calculator: \(\mathrm{20.300 \times 1,760 = 35,728}\)

Answer: 35,728 yards per hour

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may think they need to divide instead of multiply when converting units.

They might reason: "I'm going from a larger unit (miles) to a smaller unit (yards), so I should divide." This leads to calculating \(\mathrm{20.300 \div 1,760 \approx 0.0115}\), which doesn't make sense as a speed measurement and doesn't match any reasonable answer choice.

Second Most Common Error:

Poor SIMPLIFY execution: Making arithmetic errors during multiplication.

Students might set up the problem correctly but make calculation mistakes with \(\mathrm{20.300 \times 1,760}\), perhaps getting \(\mathrm{35,280}\) or \(\mathrm{37,528}\) due to misplaced digits or computational errors.

The Bottom Line:

Unit conversion problems require clear understanding of when to multiply versus divide. The key insight is recognizing that conversion factors should be set up so unwanted units cancel out, leaving only the desired units.