A tank initially holds 36 gallons of water and leaks at a rate of 11 gallons per hour. Which equation...

1. TRANSLATE the problem information

• Given information:
  • Initial amount: 36 gallons
  • Rate of loss: 11 gallons per hour
  • Time variable: t hours
  • Find: equation for amount w after t hours

2. INFER the mathematical relationship

• Since water is leaking OUT of the tank, the amount decreases over time
• After t hours, total amount lost = \(\mathrm{11\ gallons/hour \times t\ hours = 11t\ gallons}\)
• Amount remaining = Initial amount - Amount lost

3. TRANSLATE this relationship into equation form

• \(\mathrm{w = 36 - 11t}\)

Answer: D (\(\mathrm{w = 36 - 11t}\))

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't properly interpret what "leaking" means mathematically. They see rate and time together and think "\(\mathrm{rate \times time}\) gets added" without considering the direction of change.

This leads them to write \(\mathrm{w = 36 + 11t}\), making them select Choice B (\(\mathrm{w = 36 + 11t}\))

Second Most Common Error:

Poor TRANSLATE execution: Students correctly understand that water decreases, but mix up which number goes where in the equation. They might think the rate (11) should be the starting point and the initial amount (36) should be subtracted.

This may lead them to select Choice C (\(\mathrm{w = 11 - 36t}\))

The Bottom Line:

The key insight is recognizing that "leaking" or any loss scenario requires subtraction from an initial value. Rate problems aren't just about multiplying \(\mathrm{rate \times time}\)—you must consider whether that product increases or decreases your starting amount.