The chart displays the stages of Alvin's northward expedition, detailing the various segments of his journey.

Leg | Distance (km) | Time (minutes)
1 | 103 | 67
2 | 127 | 73
3 | 119 | 79
4 | 107 | 61
At which stage of his expedition did Alvin experience the highest average velocity?

1 answer

To find the stage of Alvin's expedition where he experienced the highest average velocity, we can calculate the average velocity for each leg of the journey using the formula:

\[ \text{Average Velocity} = \frac{\text{Distance}}{\text{Time}} \]

We will convert the time from minutes to hours to get the velocity in kilometers per hour (km/h).

  1. Leg 1:

    • Distance = 103 km
    • Time = 67 minutes = \( \frac{67}{60} \) hours = 1.1167 hours (approximately)
    • Average Velocity = \( \frac{103}{1.1167} \approx 92.2 \) km/h
  2. Leg 2:

    • Distance = 127 km
    • Time = 73 minutes = \( \frac{73}{60} \) hours = 1.2167 hours (approximately)
    • Average Velocity = \( \frac{127}{1.2167} \approx 104.7 \) km/h
  3. Leg 3:

    • Distance = 119 km
    • Time = 79 minutes = \( \frac{79}{60} \) hours = 1.3167 hours (approximately)
    • Average Velocity = \( \frac{119}{1.3167} \approx 90.2 \) km/h
  4. Leg 4:

    • Distance = 107 km
    • Time = 61 minutes = \( \frac{61}{60} \) hours \approx 1.0167 hours (approximately)
    • Average Velocity = \( \frac{107}{1.0167} \approx 105.2 \) km/h

Now, we can summarize the average velocities for each leg:

  • Leg 1: 92.2 km/h
  • Leg 2: 104.7 km/h
  • Leg 3: 90.2 km/h
  • Leg 4: 105.2 km/h

Conclusion: Alvin experienced the highest average velocity during Leg 4, with an average velocity of approximately 105.2 km/h.