A commercial water pump operates at a constant rate, consuming 18 gallons of fuel every hour. Given that 1 gallon...

1. TRANSLATE the problem information

• Given information:
  • Water pump rate: \(\mathrm{18\,gallons\,per\,hour}\)
  • Conversion factor: \(\mathrm{1\,gallon = 4\,quarts}\)
  • Target: rate in quarts per minute

• What this tells us: We need to convert both the volume units (gallons → quarts) and time units (hours → minutes)

2. INFER the solution strategy

• This is a two-step unit conversion problem
• First convert the volume units, then convert the time units
• We can work systematically: gallons/hour → quarts/hour → quarts/minute

3. Convert gallons to quarts

• Start with: \(\mathrm{18\,gallons\,per\,hour}\)
• Since \(\mathrm{1\,gallon = 4\,quarts}\): \(\mathrm{18 \times 4 = 72\,quarts\,per\,hour}\)

4. Convert hours to minutes

• We now have: \(\mathrm{72\,quarts\,per\,hour}\)
• Since \(\mathrm{1\,hour = 60\,minutes}\), we divide by 60: \(\mathrm{72 \div 60\,quarts\,per\,minute}\)

5. SIMPLIFY the final calculation

• \(\mathrm{72 \div 60}\)
• \(\mathrm{= \frac{72}{60}}\)
• Reduce the fraction:
• \(\mathrm{\frac{72}{60} = \frac{12}{10} = 1.2}\)

Answer: \(\mathrm{1.2}\) (or \(\mathrm{\frac{6}{5}}\))

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students often get confused about whether to multiply or divide when converting units. They might incorrectly think "since there are 60 minutes in an hour, I need to multiply by 60" instead of dividing.

This leads them to calculate: \(\mathrm{(18 \times 4 \times 60) \div 1 = 4,320\,quarts\,per\,minute}\), which is clearly unreasonable but might cause confusion and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up \(\mathrm{\frac{72}{60}}\) but make arithmetic errors in simplification. They might incorrectly simplify to \(\mathrm{1.02}\) or \(\mathrm{1.12}\), or get confused with decimal vs fraction forms.

This causes calculation errors that lead to selecting incorrect numerical answers.

The Bottom Line:

Unit conversion problems require systematic thinking about which direction each conversion should go. The key insight is recognizing that converting to smaller units (gallons to quarts) means multiplying, while converting to smaller time intervals (hours to minutes) means the rate number gets smaller, so we divide.