A water tank initially contains 40 gallons of water. Water drains from the tank at a constant rate of 4...

1. TRANSLATE the problem information

• Given information:
  • Initial amount: 40 gallons
  • Drainage rate: 4 gallons per hour (constant)
  • Need to find: Water remaining W at different times t

2. INFER the mathematical relationship

• Since water drains at a constant rate, this creates a linear relationship
• The amount remaining = Initial amount - (Rate × Time)
• Therefore: \(\mathrm{W = 40 - 4t}\)

3. SIMPLIFY by calculating values for each given time

• For \(\mathrm{t = 0}\) hours: \(\mathrm{W = 40 - 4(0)}\)
  \(\mathrm{= 40 - 0}\)
  \(\mathrm{= 40}\) gallons
• For \(\mathrm{t = 1}\) hour: \(\mathrm{W = 40 - 4(1)}\)
  \(\mathrm{= 40 - 4}\)
  \(\mathrm{= 36}\) gallons
• For \(\mathrm{t = 2}\) hours: \(\mathrm{W = 40 - 4(2)}\)
  \(\mathrm{= 40 - 8}\)
  \(\mathrm{= 32}\) gallons

4. APPLY CONSTRAINTS to select the correct table

• Look for the table showing: \(\mathrm{(0,40), (1,36), (2,32)}\)
• This matches Choice C exactly

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "drains at 4 gallons per hour" as meaning water increases by 4 gallons each hour, rather than decreases.

They might think: "4 gallons per hour means we add 4 each hour" and create the equation \(\mathrm{W = 40 + 4t}\) instead of \(\mathrm{W = 40 - 4t}\). This gives values of \(\mathrm{40, 44, 48}\) for \(\mathrm{t = 0, 1, 2}\).

This leads them to select Choice B (40, 44, 48).

Second Most Common Error:

Poor INFER reasoning: Students understand that water is draining but incorrectly think the tank starts empty and the "4 gallons per hour" represents some kind of loss that accumulates.

They might create \(\mathrm{W = -4t}\), giving values \(\mathrm{0, -4, -8}\) for \(\mathrm{t = 0, 1, 2}\), or they might think the problem is asking about total water drained rather than water remaining.

This may lead them to select Choice D (0, -4, -8) or Choice A (0, 4, 8).

The Bottom Line:

The key challenge is correctly interpreting "drains from" as subtraction from the initial amount, not addition to zero or some other starting point. Students must recognize that drainage represents a negative rate of change applied to the initial quantity.