A car normally uses 1 gallon of fuel to travel 24 miles. When using an eco-friendly driving mode, the car...

1. TRANSLATE the problem information

• Given information:
  • Normal consumption: 1 gallon for 24 miles
  • Eco-mode uses 75% of normal consumption
  • Need equation for fuel F to travel m miles in eco-mode

• What this tells us: We need to build an equation that starts with normal consumption and reduces it by 25%.

2. INFER the solution approach

• Strategy: Work in two stages
  • First, find how much fuel is needed for m miles under normal conditions
  • Then, apply the 75% reduction for eco-mode

• Why this order matters: The percentage reduction applies to whatever the normal consumption would be.

3. TRANSLATE normal consumption to mathematical form

• Normal rate: 1 gallon per 24 miles
• For m miles: \(\mathrm{m/24}\) gallons
• This gives us our baseline consumption before any eco-mode adjustment

4. INFER how to apply the percentage reduction

• "Uses only 75% of normal consumption" means multiply by 0.75
• Eco-mode fuel: \(\mathrm{0.75 \times (normal\ consumption)}\)
• Eco-mode fuel: \(\mathrm{0.75 \times (m/24) = 0.75m/24}\)

5. SIMPLIFY to match answer format

• \(\mathrm{F = 0.75m/24}\)
• This exactly matches choice (D)

Answer: D

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER reasoning: Students often confuse what the 75% applies to or how to implement the reduction.

Some students see "uses 75% less" instead of "uses 75% of normal" and calculate \(\mathrm{F = m/24 - 0.75(m/24) = 0.25m/24}\), which doesn't match any answer choice. Others might think 75% reduction means dividing by 0.75, leading to \(\mathrm{F = (m/24)/0.75 = m/18}\). This may lead them to select Choice B (\(\mathrm{F = m/18}\)).

Second Most Common Error:

Poor TRANSLATE skills: Students misread the problem setup and use the wrong baseline consumption.

They might forget that normal consumption is \(\mathrm{m/24}\) gallons and instead think it's \(\mathrm{24m}\) gallons (confusing miles per gallon with gallons per mile). Applying 75% to this gives \(\mathrm{F = 0.75(24m) = 18m}\), which is closest to Choice C (\(\mathrm{F = 24m}\)) among the wrong interpretations.

The Bottom Line:

This problem requires careful attention to what the percentage reduction applies to (the normal fuel consumption, not the distance) and precise translation of the consumption rate relationship.