To qualify for a sprint final, an athlete's time must be at most 12.50 seconds. In a preliminary heat, the...

1. TRANSLATE the problem information

• Given information:
  • Qualifying time: at most 12.50 seconds
  • Current time: 13.18 seconds
  • Find: how many seconds to reduce

• What this tells us: We need to find the difference between the current time and the qualifying threshold

2. INFER the approach

• Since "at most 12.50 seconds" means the time must be \(\leq \mathrm{12.50}\), the minimum reduction needed brings the athlete exactly to 12.50 seconds
• Strategy: Subtract the qualifying time from the current time

3. SIMPLIFY the calculation

• Time reduction needed = \(\mathrm{13.18 - 12.50 = 0.68}\) seconds
• Verification: \(\mathrm{13.18 - 0.68 = 12.50}\) ✓ (meets the requirement)

Answer: 0.68 seconds (Choice C)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make decimal subtraction errors, such as incorrectly aligning decimal places or making borrowing mistakes.

For example, they might calculate \(\mathrm{13.18 - 12.50}\) as 0.62 instead of 0.68, possibly by incorrectly handling the borrowing in the tenths place (8 - 0 = 8, but 1 - 5 requires borrowing).

This may lead them to select Choice B (0.62)

Second Most Common Error:

Poor TRANSLATE reasoning: Students might misunderstand what "by how many seconds must reduce" means and attempt to calculate \(\mathrm{12.50 - 13.18}\), getting a negative result, then take the absolute value or add numbers incorrectly to get a positive answer.

This leads to confusion and potentially guessing among the positive answer choices.

The Bottom Line:

This problem tests careful decimal arithmetic more than complex reasoning. The key insight is recognizing that "reduce by" means finding how much to subtract from the current time to reach the target.