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

Answer 1

The Correct Option is A

Step 1: Define the total distance 

Let the total distance be:

\[ d = 778 \text{ km} \]

Step 2: Calculate the time taken to travel from A to B

\[ \frac{d}{84} = \frac{778}{84} = 9.26 \text{ hours} \]

Step 3: Calculate the time taken to return from B to A

\[ \frac{d}{56} = \frac{778}{56} = 13.89 \text{ hours} \]

Step 4: Calculate the total time for the journey

\[ 9.26 + 13.89 = 23.15 \text{ hours} \]

Step 5: Calculate the total distance traveled

\[ 2d = 2 \times 778 = 1556 \text{ km} \]

Step 6: Calculate the average speed

\[ \frac{\text{Total distance}}{\text{Total time}} = \frac{1556}{23.15} = 67.2 \text{ km/h} \]

Thus, the average speed is 67.2 km/h.