A large water tank initially contains 200 gallons of water. Water is drained from the tank at a constant rate...

1. TRANSLATE the problem information

• Given information:
  • Initial water: 200 gallons
  • Drainage rate: 10 gallons per minute
  • Time: m minutes
  • Find: W (gallons remaining after m minutes)

2. TRANSLATE the rate into total amount

• After m minutes of draining at 10 gallons/minute:
  • Total amount drained = \(10 \times \mathrm{m} = 10\mathrm{m}\) gallons

3. INFER the relationship for remaining water

• The key insight: Remaining water = What you started with - What you've lost
• \(\mathrm{W} = \text{Initial amount} - \text{Total amount drained}\)
• \(\mathrm{W} = 200 - 10\mathrm{m}\)

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse whether the drainage should be added or subtracted from the initial amount.

They might think: "The tank has 200 gallons, and we're adding 10 gallons per minute of activity," misunderstanding that drainage means water is leaving the tank, not entering it.

This may lead them to select Choice A (\(\mathrm{W} = 200 + 10\mathrm{m}\))

Second Most Common Error:

Poor TRANSLATE reasoning: Students correctly understand subtraction is needed but get confused about which quantity should be subtracted from which.

They might think: "We need 10m minus something," focusing on the rate term first instead of starting with the initial amount.

This may lead them to select Choice C (\(\mathrm{W} = 10\mathrm{m} - 200\))

The Bottom Line:

The key insight is recognizing that drainage reduces the amount in the tank over time. Students who miss this fundamental direction of change will set up their equation incorrectly, regardless of their algebraic skills.