Calculate George's Average Speed: Journey Details of 82 km/h for 4 Hours and 70 km/h for 3 Hours

To solve this problem, we'll follow these steps:

• Step 1: Calculate the distance for each part of the journey.
• Step 2: Find the total distance traveled.
• Step 3: Convert all time to hours and include the break time.
• Step 4: Calculate the average speed using the formula for average speed.

Let's calculate each step:

Step 1: Calculate the distances:
For the first part of the journey:
Speed = 82 km/h, Time = 4 hours
Distance = Speed × Time = $82 \times 4 = 328$ km

For the second part of the journey:
Speed = 70 km/h, Time = 3 hours
Distance = Speed × Time = $70 \times 3 = 210$ km

Step 2: Total distance traveled:
Total Distance = Distance of first part + Distance of second part
Total Distance = $328 + 210 = 538$ km

Step 3: Calculate total time including the break:
Total time driving = 4 hours (first part) + 3 hours (second part) = 7 hours

Break time = 20 minutes = $\frac{20}{60} = \frac{1}{3}$ hours

Total time = Driving time + Break time = $7 + \frac{1}{3} = \frac{22}{3}$ hours

Step 4: Calculate the average speed:
Average speed $v_{avg} = \frac{\text{Total distance}}{\text{Total time}}$
Average speed $v_{avg} = \frac{538}{\frac{22}{3}} = 538 \times \frac{3}{22} = \frac{538 \times 3}{22} = \frac{1614}{22}$

Simplifying $\frac{1614}{22}$: Average speed ≈ $73.36$ km/h

Therefore, the average speed of George's truck for the entire journey, including the break, is $73.36$ km/h.