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
  • Need to find: minutes spent walking

• Let \(\mathrm{j}\) = minutes jogging and \(\mathrm{w}\) = minutes walking

2. TRANSLATE the relationships into equations

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

3. INFER the solution strategy

• We have two equations with two unknowns - this is a system of linear equations
• Substitution method will work well since the first equation easily gives us \(\mathrm{w}\) in terms of \(\mathrm{j}\)

4. SIMPLIFY using substitution

• From \(\mathrm{j + w = 21}\), we get: \(\mathrm{w = 21 - j}\)
• Substitute into distance equation: \(\mathrm{80j + 60(21 - j) = 1,440}\)
• Expand: \(\mathrm{80j + 1,260 - 60j = 1,440}\)
• Combine like terms: \(\mathrm{20j = 1,440 - 1,260 = 180}\)
• Solve: \(\mathrm{j = 9}\) minutes

5. SIMPLIFY to find walking time

• \(\mathrm{w = 21 - j = 21 - 9 = 12}\) minutes

Answer: C (12)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students often confuse which variable represents what they're solving for. They might set up equations correctly but then solve for jogging time and mistakenly select that as their final answer.

Since \(\mathrm{j = 9}\), they incorrectly choose Choice B (9) instead of recognizing they need \(\mathrm{w = 12}\).

Second Most Common Error:

Poor SIMPLIFY execution: Students make algebraic errors when expanding \(\mathrm{60(21 - j)}\), getting the wrong coefficient for \(\mathrm{j}\) or making arithmetic mistakes with 1,260.

A common mistake is: \(\mathrm{80j + 60(21 - j) = 80j + 1,260 + 60j = 140j + 1,260}\), leading to incorrect solutions and confusion about which answer choice to select.

The Bottom Line:

This problem tests whether students can systematically translate a word problem into equations AND carefully track what variable they're actually solving for. The key insight is recognizing that finding "minutes walking" means you need the \(\mathrm{w}\)-value, not the \(\mathrm{j}\)-value you solve for first.