Understanding Electric Bus Data and Efficiency

The problem asks us to identify the specific stretch of travel (M, N, O, or P) where the electricity consumption per km is the minimum for an electric bus. We are provided with cumulative data for both the distance travelled and the electricity consumed. To find the consumption for each individual stretch, we need to calculate the difference in cumulative values between the start and end points of that stretch.

Analyzing Cumulative Electricity Consumption and Distance

The provided table shows cumulative values. This means the values for stretch N include the travel for stretch M, and so on. To find the actual distance covered and electricity consumed for each individual stretch, we must subtract the cumulative values of the preceding stretch.

Calculating Individual Stretch Electricity and Distance

Let's calculate the actual distance travelled and electricity consumed for each individual stretch (M, N, O, P):

• Stretch M:
  • Distance travelled: \(20 \text{ km}\) (since it's the first stretch)
  • Electricity consumed: \(12 \text{ kWh}\) (since it's the first stretch)
• Stretch N:
  • Distance travelled: \(45 \text{ km} - 20 \text{ km} = 25 \text{ km}\)
  • Electricity consumed: \(25 \text{ kWh} - 12 \text{ kWh} = 13 \text{ kWh}\)
• Stretch O:
  • Distance travelled: \(75 \text{ km} - 45 \text{ km} = 30 \text{ km}\)
  • Electricity consumed: \(45 \text{ kWh} - 25 \text{ kWh} = 20 \text{ kWh}\)
• Stretch P:
  • Distance travelled: \(100 \text{ km} - 75 \text{ km} = 25 \text{ km}\)
  • Electricity consumed: \(57 \text{ kWh} - 45 \text{ kWh} = 12 \text{ kWh}\)

Determining Electricity Consumption Per KM

Now, we will calculate the electricity consumption per km for each individual stretch by dividing the electricity consumed by the distance travelled in that stretch.

• Stretch M:
  • Consumption per km = \(\frac{12 \text{ kWh}}{20 \text{ km}} = 0.6 \text{ kWh/km}\)
• Stretch N:
  • Consumption per km = \(\frac{13 \text{ kWh}}{25 \text{ km}} = 0.52 \text{ kWh/km}\)
• Stretch O:
  • Consumption per km = \(\frac{20 \text{ kWh}}{30 \text{ km}} \approx 0.6667 \text{ kWh/km}\)
• Stretch P:
  • Consumption per km = \(\frac{12 \text{ kWh}}{25 \text{ km}} = 0.48 \text{ kWh/km}\)

Comparing Electricity Consumption Values

Let's summarize the electricity consumption per km for all stretches:

By comparing these values, we can clearly see which stretch has the minimum electricity consumption per km.

• \(0.6 \text{ kWh/km}\) (M)
• \(0.52 \text{ kWh/km}\) (N)
• \(0.6667 \text{ kWh/km}\) (O)
• \(0.48 \text{ kWh/km}\) (P)

The minimum value among these is \(0.48 \text{ kWh/km}\), which corresponds to Stretch P.

Conclusion: Most Efficient Stretch

Based on our calculations, the stretch where the electricity consumption per km is minimum is Stretch P. This indicates that Stretch P was the most energy-efficient part of the bus's journey during this operation.