At a conference, a coordinator schedules s short talks, each lasting 20 minutes, and l long talks, each lasting 50...

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{s}\) = number of short talks
  • Each short talk lasts 20 minutes
  • \(\mathrm{l}\) = number of long talks
  • Each long talk lasts 50 minutes
  • Total time for all talks = 440 minutes
• The word "each" tells us we need to multiply the number of talks by their individual durations

2. INFER how to find total time

• Total time = Time from all short talks + Time from all long talks
• For short talks: \(\mathrm{s}\) talks × 20 minutes each = \(\mathrm{20s}\) minutes
• For long talks: \(\mathrm{l}\) talks × 50 minutes each = \(\mathrm{50l}\) minutes

3. TRANSLATE the relationship into an equation

• Total time = \(\mathrm{20s + 50l}\)
• Since total time equals 440 minutes: \(\mathrm{20s + 50l = 440}\)

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students recognize they need an equation but don't properly convert "each lasting [time]" into multiplication.

They might think the problem is just asking about the number of talks total, leading them to write \(\mathrm{s + l = 440}\), or they might partially translate by only multiplying one type of talk by its duration (like \(\mathrm{20s + l = 440}\)).

This may lead them to select Choice A (\(\mathrm{s + l = 440}\)) or Choice B (\(\mathrm{20s + l = 440}\))

The Bottom Line:

The key challenge is recognizing that "each lasting [duration]" requires multiplying the quantity by the unit value. Students often focus on the numbers of items rather than the total time those items represent.