A storage tank initially contains 250 gallons of water. Water is pumped out of the tank at a constant rate...

1. TRANSLATE the problem information

• Given information:
  • Initial water: 250 gallons
  • Pumping rate: 12 gallons per hour
  • Time period: h hours
  • Final water: 70 gallons

• What this tells us: We need an equation showing how the initial amount changes over time.

2. INFER the mathematical relationship

• Key insight: When water is "pumped out," we're removing it from the tank
• This means: Starting amount - Amount removed = Ending amount
• Amount removed = Rate × Time = \(\mathrm{12h}\) gallons total

3. Set up the equation

• Using our relationship: \(\mathrm{250 - 12h = 70}\)
• This matches choice (D)

Answer: D

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "pumped out" and use addition instead of subtraction

When students see "water is pumped out," they might think about the action of pumping as adding something to the situation, rather than recognizing that pumping out means removing water from the tank. This leads them to write: \(\mathrm{250 + 12h = 70}\)

This may lead them to select Choice C (\(\mathrm{250 + 12h = 70}\))

Second Most Common Error:

Poor TRANSLATE reasoning: Students confuse which quantities go where in the equation structure

Some students understand that subtraction is needed but get confused about the equation setup. They might think the amount removed minus what remains equals the original amount, leading to: \(\mathrm{12h - 70 = 250}\)

This may lead them to select Choice A (\(\mathrm{12h - 70 = 250}\))

The Bottom Line:

The key challenge is recognizing that "pumped out" means subtraction and maintaining clear thinking about what each quantity represents in the final equation structure.