A water storage tank initially contains 240 gallons of water. Water drains from the tank at a constant rate of...

1. TRANSLATE the problem information

• Given information:
  • Initial amount: 240 gallons
  • Drainage rate: 6 gallons per minute
  • Time variable: m minutes
  • Find: amount w remaining after m minutes

2. INFER the mathematical relationship

• Since water drains OUT, the amount decreases over time
• After m minutes, total drained = \(\mathrm{6 × m = 6m}\) gallons
• Amount remaining = What we started with - What we lost

3. Build the equation

• Starting amount: \(\mathrm{240}\)
• Amount lost: \(\mathrm{6m}\)
• Amount remaining: \(\mathrm{w = 240 - 6m}\)

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "drains from" and think water is being added rather than removed.

They reason: "6 gallons per minute means we add \(\mathrm{6m}\) to what we have," leading to \(\mathrm{w = 6m + 240}\).

This may lead them to select Choice B \(\mathrm{(6m + 240)}\)

Second Most Common Error:

Poor INFER reasoning: Students correctly identify that water decreases but confuse which quantity should be multiplied by time.

They think: "240 changes over time" instead of recognizing that the rate (6 gallons/minute) multiplied by time gives the total drainage.

This may lead them to select Choice C \(\mathrm{(240m - 6)}\)

The Bottom Line:

This problem tests whether students can correctly translate rate language into mathematical operations and understand that a drainage rate means subtraction from an initial amount.