A triathlon is a multisport race consisting of three different legs. A triathlon participant completed the cycling leg with an...

1. TRANSLATE the problem information

• Given information:
  • Speed during cycling leg: \(19.700\text{ miles per hour}\)
  • Conversion factor: \(1\text{ mile} = 1{,}760\text{ yards}\)
• Find: Speed in yards per hour

2. INFER the conversion strategy

• To convert from miles per hour to yards per hour, we need dimensional analysis
• We'll multiply by the conversion factor arranged so miles cancel out: \(\frac{1{,}760\text{ yards}}{1\text{ mile}}\)
• This will change miles to yards while keeping the "per hour" the same

3. SIMPLIFY using dimensional analysis

• Set up the conversion: \(\frac{19.700\text{ miles}}{\text{hour}} \times \frac{1{,}760\text{ yards}}{1\text{ mile}}\)
• The "miles" units cancel: \(19.700 \times 1{,}760\text{ yards/hour}\)
• Calculate: \(19.700 \times 1{,}760 = 34{,}672\) (use calculator)

Answer: 34,672 yards per hour

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students often divide instead of multiply when converting units, thinking "since yards are smaller than miles, I should divide."

They might calculate: \(19.700 \div 1{,}760 = 0.0112\text{ yards per hour}\), which doesn't make sense but leads to confusion and guessing.

Second Most Common Error:

Poor TRANSLATE reasoning: Students may not clearly understand what "in yards per hour" means and might try to convert just the numerical value without considering the units properly.

This leads to random manipulation of numbers without systematic conversion, causing them to get stuck and guess.

The Bottom Line:

This problem tests whether students understand that unit conversion requires systematic dimensional analysis - multiplying by conversion factors arranged to cancel unwanted units. The key insight is that we're converting the distance unit (miles to yards) while keeping the time unit (hours) the same.