A portable generator has a fuel tank that holds 24 gallons when full. During operation, the generator consumes fuel at...
GMAT Algebra : (Alg) Questions
A portable generator has a fuel tank that holds \(\mathrm{24}\) gallons when full. During operation, the generator consumes fuel at a constant rate of exactly \(\mathrm{2.4}\) gallons per hour. Which of the following functions best models the amount of fuel remaining in the tank, in gallons, after \(\mathrm{h}\) hours of operation, where \(\mathrm{h = 1, 2, 3, 4, 5}\)?
1. TRANSLATE the problem information
- Given information:
- Tank capacity: 24 gallons when full
- Consumption rate: 2.4 gallons per hour (constant)
- Need function for fuel remaining after h hours
- What this tells us: We start with 24 gallons and lose 2.4 gallons each hour.
2. INFER the mathematical relationship
- Key insight: Remaining fuel = Starting fuel - Fuel consumed
- Since fuel is consumed at 2.4 gallons per hour, after h hours the total consumed is \(\mathrm{2.4h}\) gallons
- Therefore: \(\mathrm{f(h) = 24 - 2.4h}\)
3. Verify with specific values
- After 1 hour: \(\mathrm{f(1) = 24 - 2.4(1) = 21.6}\) gallons remaining ✓
- After 2 hours: \(\mathrm{f(2) = 24 - 2.4(2) = 19.2}\) gallons remaining ✓
- After 5 hours: \(\mathrm{f(5) = 24 - 2.4(5) = 12}\) gallons remaining ✓
The fuel decreases as expected, confirming our function is correct.
Answer: C
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Not recognizing that fuel consumption means the amount decreases over time.
Students may think of "2.4 gallons per hour" as fuel being added rather than consumed, leading them to write \(\mathrm{f(h) = 24 + 2.4h}\) instead of \(\mathrm{f(h) = 24 - 2.4h}\).
This may lead them to select Choice A (\(\mathrm{f(h) = 24 + 2.4h}\)).
Second Most Common Error:
Poor TRANSLATE reasoning: Confusing which quantity should be multiplied by time.
Students might think the initial 24 gallons should be multiplied by hours, creating functions like \(\mathrm{f(h) = 24h - 2.4}\) or \(\mathrm{f(h) = 24h + 2.4}\), rather than recognizing that only the consumption rate (2.4) gets multiplied by time.
This may lead them to select Choice B (\(\mathrm{f(h) = 24h - 2.4}\)) or Choice D (\(\mathrm{f(h) = 24h + 2.4}\)).
The Bottom Line:
This problem tests whether students can correctly model a decreasing linear relationship and understand that consumption means subtraction, not addition.