A runner completes a 21-minute workout consisting only of jogging and walking. When jogging, the runner moves at a constant...

1. TRANSLATE the problem information

• Given information:
  • Total workout time: 21 minutes
  • Jogging speed: 80 meters per minute
  • Walking speed: 60 meters per minute
  • Total distance: 1,440 meters
  • Find: minutes spent walking
• What this tells us: We have two constraints that must be satisfied simultaneously

2. INFER the mathematical approach

• This is a system of equations problem with two unknowns
• Strategy: Set up equations for time constraint and distance constraint
• Let \(j\) = minutes jogging, \(w\) = minutes walking

3. TRANSLATE constraints into equations

• Time constraint: \(j + w = 21\)
• Distance constraint: \(80j + 60w = 1,440\)

4. SIMPLIFY by solving the system

• From the time equation: \(j = 21 - w\)
• Substitute into distance equation: \(80(21 - w) + 60w = 1,440\)
• Expand: \(1,680 - 80w + 60w = 1,440\)
• Combine like terms: \(1,680 - 20w = 1,440\)
• Solve: \(-20w = -240\), so \(w = 12\)

5. Verify the solution

• If \(w = 12\), then \(j = 21 - 12 = 9\)
• Distance check: \(80(9) + 60(12) = 720 + 720 = 1,440\) ✓

Answer: C (12)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students often struggle to correctly set up the two equations from the word problem description. They might confuse the relationship between distance, rate, and time, or incorrectly assign variables to jogging vs walking.

For example, they might write the distance equation as \(60j + 80w = 1,440\) (switching the rates), or set up \(j + w = 1,440\) (confusing time and distance constraints). This leads to incorrect equations and wrong solutions.

This may lead them to select Choice A (3) or cause confusion and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up the equations but make algebraic mistakes during the solution process. Common errors include sign errors when distributing, combining like terms incorrectly, or solving for j instead of w.

Some students solve correctly but answer the wrong question - finding \(j = 9\) and selecting Choice B (9) instead of recognizing the question asks for walking time \(w = 12\).

The Bottom Line:

This problem tests whether students can translate a real-world scenario into mathematical equations and systematically solve them. The key challenge is maintaining accuracy through both the setup and algebraic solution phases while keeping track of what the question is actually asking for.