Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back B to A with a uniform speed of 56 km per hour. Find the average speed of the train during the whole journey.

Answer

To find the average speed of the train during the whole journey from station A to station B and back, we can follow these steps:

### Step 1: Identify the distances and speeds
- Distance from A to B = 778 km
- Speed from A to B = 84 km/h
- Speed from B to A = 56 km/h

### Step 2: Calculate the time taken for each part of the journey
- Time taken from A to B:
\[ \text{Time}_{AB} = \frac{\text{Distance}}{\text{Speed}} = \frac{778 \text{ km}}{84 \text{ km/h}} = \frac{778}{84} \approx 9.26 \text{ hours} \]

- Time taken from B to A:
\[ \text{Time}_{BA} = \frac{778 \text{ km}}{56 \text{ km/h}} = \frac{778}{56} \approx 13.89 \text{ hours} \]

### Step 3: Calculate the total time for the whole journey
- Total time:
\[ \text{Total Time} = \text{Time}_{AB} + \text{Time}_{BA} \approx 9.26 + 13.89 \approx 23.15 \text{ hours} \]

### Step 4: Calculate the total distance for the whole journey
- Total distance:
\[ \text{Total Distance} = 778 \text{ km} + 778 \text{ km} = 1556 \text{ km} \]

### Step 5: Calculate the average speed
- Average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{1556 \text{ km}}{23.15 \text{ hours}} \approx 67.2 \text{ km/h} \]

### Final Answer
The average speed of the train during the whole journey is approximately **67.2 km/h**.

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