Automated packaging line P processed a total of 150 boxes on Tuesday. On the same day, automated packaging line Q...

1. TRANSLATE the problem information

• Given information:
  • Line P: 150 boxes total on Tuesday
  • Line Q: 20 boxes per hour for 3 hours on Tuesday
  • Find: Total boxes from both lines

• What this tells us: We need to find two separate amounts, then combine them.

2. INFER the approach

• This is a two-part problem: calculate line Q's production, then add both lines together
• Line P's amount is given directly, but line Q requires a rate calculation
• The word "total" means we add the results from both lines

3. Calculate line Q's production

• Line Q worked at 20 boxes per hour for 3 hours
• Using the rate formula: \(\mathrm{20\ boxes/hour \times 3\ hours = 60\ boxes}\)

4. TRANSLATE "total boxes processed by both lines"

• This means: Line P boxes + Line Q boxes
• \(\mathrm{Total = 150 + 60 = 210\ boxes}\)

Answer: D (210)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread the problem structure and try to combine all the given numbers incorrectly.

Instead of recognizing that line Q requires a rate calculation first, they might add \(\mathrm{150 + 20 + 3 = 173}\), thinking all three numbers should be combined directly. This leads them to select Choice C (173).

Second Most Common Error:

Incomplete solution due to poor INFER reasoning: Students calculate only one line's production and stop there.

They might calculate line Q correctly (\(\mathrm{20 \times 3 = 60}\)) but forget to add line P's 150 boxes, or they might just use line P's 150 boxes and ignore line Q entirely. This incomplete approach could lead them to select Choice B (170) if they somehow add an incorrect partial calculation.

The Bottom Line:

This problem tests whether students can handle multi-step word problems involving rates. The key challenge is recognizing that "total from both lines" requires two separate calculations followed by addition, not simply combining all visible numbers.