A water tank initially contains 8 gallons of water. Water is added at a constant rate according to the equation...
GMAT Algebra : (Alg) Questions
A water tank initially contains 8 gallons of water. Water is added at a constant rate according to the equation \(\mathrm{V = 8 + 6t}\), where \(\mathrm{V}\) is the total volume in gallons and \(\mathrm{t}\) is the time in hours. How many gallons of water will be in the tank after 5 hours?
1. TRANSLATE the problem information
- Given information:
- Initial water: 8 gallons
- Equation: \(\mathrm{V = 8 + 6t}\) (V = total volume in gallons, t = time in hours)
- Find: Volume after 5 hours
- What this tells us: We need to substitute \(\mathrm{t = 5}\) into the given equation to find the total volume.
2. TRANSLATE the time requirement
- "After 5 hours" means \(\mathrm{t = 5}\)
- We substitute this value into our equation \(\mathrm{V = 8 + 6t}\)
3. SIMPLIFY through substitution and calculation
- Substitute \(\mathrm{t = 5}\): \(\mathrm{V = 8 + 6(5)}\)
- Calculate the multiplication first: \(\mathrm{6 × 5 = 30}\)
- Add to get the final volume: \(\mathrm{V = 8 + 30 = 38}\) gallons
Answer: D (38 gallons)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misunderstand what the equation represents or how to substitute the time value.
Some students might think the \(\mathrm{6t}\) term means "6 plus t" instead of "6 times t," leading them to calculate \(\mathrm{V = 8 + 6 + 5 = 19}\) (though this isn't an answer choice). Others might substitute incorrectly, using just the coefficient 6 instead of \(\mathrm{6t}\), calculating \(\mathrm{V = 8 + 6 = 14}\).
This may lead them to select Choice B (14).
Second Most Common Error:
Incomplete SIMPLIFY execution: Students correctly identify \(\mathrm{t = 5}\) but make arithmetic errors or only calculate part of the problem.
Some students might calculate only the rate portion (\(\mathrm{6 × 5 = 30}\)) and forget to add the initial 8 gallons, or they might add \(\mathrm{8 + 5 = 13}\) instead of properly substituting into \(\mathrm{6t}\).
This may lead them to select Choice A (13) or Choice C (30).
The Bottom Line:
This problem tests whether students can properly interpret and use a linear function in a real-world context. The key is understanding that the equation gives you the total volume at any time t, not just the amount being added.