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).
-
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
-
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
-
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
-
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.