A water tank is being filled at a constant rate. After 6 minutes, the tank contains 42 liters of water....

1. TRANSLATE the problem information

• Given information:
  • Water tank filled at constant rate
  • After 6 minutes: tank contains 42 liters
  • Find: time to fill 70 liters at same rate

• What this tells us: We have a direct proportional relationship between time and amount of water.

2. INFER the solution strategy

• Key insight: Since the rate is constant, we first need to find how fast the tank fills (liters per minute)
• Strategy: Calculate rate, then use it to find time for 70 liters

3. SIMPLIFY to find the filling rate

• \(\mathrm{Rate = Amount \div Time}\)
• \(\mathrm{Rate = 42\,liters \div 6\,minutes = 7\,liters\,per\,minute}\)

4. SIMPLIFY to find time for 70 liters

• \(\mathrm{Time = Amount \div Rate}\)
• \(\mathrm{Time = 70\,liters \div 7\,liters\,per\,minute = 10\,minutes}\)

Answer: B (10 minutes)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret the problem as asking "how much more time" beyond the initial 6 minutes, rather than the total time from start to finish.

They might calculate: \(\mathrm{70 - 42 = 28}\) liters remaining, then \(\mathrm{28 \div 7 = 4}\) more minutes, giving \(\mathrm{6 + 4 = 10}\) minutes. While this happens to give the correct answer, the reasoning shows they didn't properly understand what the problem was asking.

Second Most Common Error:

Poor INFER reasoning: Students attempt to set up a proportion incorrectly, such as \(\mathrm{\frac{6}{42} = \frac{x}{70}}\), which would give \(\mathrm{x = 10}\). Again, this yields the correct answer by coincidence, but shows they're not thinking about rates properly.

The Bottom Line:

This problem tests whether students can identify the constant rate as the key relationship and apply it systematically, rather than getting lucky with incorrect proportional reasoning.