An electric vehicle started a highway trip with its battery at 95% charge. After driving for 180 minutes, the battery...

1. TRANSLATE the problem information

• Given information:
  • Starting battery charge: \(95\%\)
  • Ending battery charge: \(23\%\)
  • Time elapsed: \(180\) minutes
  • Total battery capacity: \(75\) kWh
  • Need to find: average rate of energy consumption in kWh per minute
• What this tells us: We need to find how much energy was consumed and divide by the time to get the rate.

2. TRANSLATE what energy was consumed

• Battery charge decreased from \(95\%\) to \(23\%\)
• Energy consumed = \(95\% - 23\% = 72\%\) of the total capacity
• This means \(72\%\) of the \(75\) kWh battery was used

3. SIMPLIFY to find actual energy consumed

• Convert percentage to actual energy: \(72\% \times 75\) kWh
• \(72\% = 0.72\), so: \(0.72 \times 75 = 54\) kWh (use calculator)
• The vehicle consumed \(54\) kWh of energy during the trip

4. SIMPLIFY to calculate the consumption rate

• Rate = Total energy consumed ÷ Time
• Rate = \(54\) kWh ÷ \(180\) minutes = \(0.30\) kWh per minute (use calculator)

Answer: (A) 0.30

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students correctly identify that \(54\) kWh was consumed but fail to complete the final step of dividing by time to find the rate.

They calculate \(72\%\) of \(75\) kWh = \(54\) kWh and think this is the final answer, not realizing they need to find consumption per minute. This may lead them to select Choice D (54.0).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misunderstand which percentages to work with, either adding \(95\% + 23\% = 118\%\) or using the wrong percentage calculation.

This leads to incorrect energy consumption values and subsequently wrong rate calculations. This causes confusion and typically results in guessing among the remaining choices.

The Bottom Line:

This problem requires careful attention to units and completing all steps of a multi-step rate calculation. Students often get the right intermediate answer (\(54\) kWh consumed) but forget that rates require division by time.