Question

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 to A with a uniform speed of 56 km per hour. Find the average speed of the train during the whole journey.

• A. \( 67.2 \)
• B. \( 76.2 \)
• C. \( 66.1 \)
• D. \( 70 \)
• E.

Hint:

For average speed over a round trip, use the formula: \[ \text{Average speed} = \frac{2 \times \text{Speed 1} \times \text{Speed 2}}{\text{Speed 1} + \text{Speed 2}} \]

Answer 1

The Correct Option is A

Let the total distance between points A and B be \( d = 778 \, \text{km} \). 

Step 1: Calculate the time taken to travel from A to B: \[ \frac{d}{84} = \frac{778}{84} \approx 9.26 \, \text{hours} \] 

Step 2: Calculate the time taken to return from B to A: \[ \frac{d}{56} = \frac{778}{56} \approx 13.89 \, \text{hours} \] 

Step 3: Calculate the total time for the entire journey: \[ 9.26 + 13.89 = 23.15 \, \text{hours} \] 

Step 4: Calculate the total distance traveled: \[ 2d = 2 \times 778 = 1556 \, \text{km} \] 

Step 5: Calculate the average speed: \[ \frac{\text{Total distance}}{\text{Total time}} = \frac{1556}{23.15} \approx 67.2 \, \text{km/h} \] Thus, the average speed is approximately 67.2 km/h.