Maya maintains a steady running pace of 9 minutes per kilometer. She plans to cover at least 14 kilometers during...

1. TRANSLATE the problem information

• Given information:
  • Maya's pace: 9 minutes per kilometer
  • Goal: at least 14 kilometers
  • Find: minimum number of minutes

• This tells us we have a rate problem involving time, speed, and distance.

2. INFER the approach

• We need to use the rate formula: \(\mathrm{Time = rate \times distance}\)
• Key insight: "at least 14 kilometers" means she could run 14 km or more, but we want the minimum time, which occurs at exactly 14 km

3. SIMPLIFY using the rate formula

• \(\mathrm{Time = pace \times distance}\)
• \(\mathrm{Time = 9\text{ minutes/km} \times 14\text{ km} = 126\text{ minutes}}\)

Answer: D. 126

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students misunderstand what "minimum time" means in the context of "at least 14 kilometers." They might think they need to find some time less than what it takes to run 14 km, not realizing that the minimum time to meet the goal of "at least 14 km" occurs when running exactly 14 km.

This confusion leads them to look for an answer smaller than 126, potentially selecting Choice A (90) or Choice B (108).

Second Most Common Error:

Poor TRANSLATE reasoning: Students might confuse which values to multiply, potentially calculating \(\mathrm{14 \div 9}\) instead of \(\mathrm{14 \times 9}\), or mixing up the rate relationship entirely.

This computational error leads to incorrect values and guessing among the answer choices.

The Bottom Line:

This problem requires students to correctly interpret rate relationships and understand that optimization language like "at least" and "minimum" work together - the minimum time to achieve "at least 14 km" happens at exactly 14 km.