A tank contains 150 liters of water at time t = 0, and the water drains at a constant rate...

1. TRANSLATE the problem information

• Given information:
  • Initial amount: 150 liters at t = 0
  • Drainage rate: 9 liters per minute (constant)
  • \(\mathrm{W(t)}\) = amount of water after t minutes
• Find: \(\mathrm{W(8)}\)

2. INFER the mathematical relationship

• Since the drainage rate is constant, this creates a linear function
• We start with 150 liters and lose 9 liters each minute
• This gives us: \(\mathrm{W(t) = 150 - 9t}\)
• Note the negative sign because water is draining out (decreasing)

3. SIMPLIFY by evaluating the function

• Substitute t = 8 into our equation:
  \(\mathrm{W(8) = 150 - 9(8)}\)
• Calculate: \(\mathrm{W(8) = 150 - 72 = 78}\)

Answer: B. 78

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students might add instead of subtract, writing \(\mathrm{W(t) = 150 + 9t}\)

Their reasoning: "The problem mentions 150 liters and 9 liters per minute, so I add them together."

This misses that drainage decreases the water amount. Using \(\mathrm{W(8) = 150 + 9(8) = 150 + 72 = 222}\), they would select Choice E (222).

Second Most Common Error:

Inadequate SIMPLIFY execution: Students set up the equation correctly but make arithmetic errors

They might calculate \(\mathrm{W(8) = 150 - 9(8)}\) but then compute 9 × 8 incorrectly, or make subtraction errors in the final step. Depending on the specific mistake, this could lead to selecting any of the incorrect answer choices.

The Bottom Line:

This problem tests whether students can recognize that "draining at a constant rate" creates a linear function with a negative slope, then execute the arithmetic correctly. The key insight is that drainage reduces the initial amount over time.