A water tank initially contains 600 gallons of water. A pump is turned on and adds water to the tank...

1. TRANSLATE the problem information

• Given information:
  • Initial water volume: 600 gallons
  • Pump adds water at: 75 gallons per minute
  • Target volume: 3,000 gallons
  • Find: Time in minutes to reach target

• What this tells us: This is a linear growth situation where volume increases at a constant rate.

2. INFER the mathematical relationship

• Since water is added at a constant rate, the volume follows a linear pattern
• At any time t, total volume = initial amount + (rate × time)
• This gives us the equation: \(\mathrm{V = 600 + 75t}\)

3. TRANSLATE the question into an equation

• We want to find t when V = 3,000 gallons
• Substitute: \(\mathrm{3{,}000 = 600 + 75t}\)

4. SIMPLIFY to solve for t

• Subtract 600 from both sides: \(\mathrm{3{,}000 - 600 = 75t}\)
• This gives us: \(\mathrm{2{,}400 = 75t}\)
• Divide both sides by 75: \(\mathrm{t = 2{,}400 \div 75}\) (use calculator if needed)
• \(\mathrm{t = 32}\)

Answer: B. 32

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students often set up the equation incorrectly as \(\mathrm{V = 75t}\), completely forgetting about the initial 600 gallons already in the tank.

When they solve \(\mathrm{3{,}000 = 75t}\), they get \(\mathrm{t = 40}\) minutes.
This may lead them to select Choice D (40).

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up \(\mathrm{V = 600 + 75t}\) and get to \(\mathrm{2{,}400 = 75t}\), but make arithmetic errors when dividing \(\mathrm{2{,}400 \div 75}\).

Common wrong calculations include getting 24 or 36 instead of 32.
This may lead them to select Choice A (24) or Choice C (36).

The Bottom Line:

This problem tests whether students can properly model a linear growth situation. The key insight is recognizing that the tank doesn't start empty—the initial 600 gallons must be included in the equation. Students who miss this fundamental setup error will consistently arrive at the wrong answer, no matter how well they execute the algebra.