A train covers a distance of 3584 km in 2 days 8 hours . If it covers 1440 km on the first day and 1608 km on the second day , by how much does the average speed of the train for the remaining part of the journey differ from that for the entire journey ?

Options

A. 3 km / hour more
B. 3 km/ hour less
C. 4 km/hour more
D. 5 km /hour less

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Calculate the total distance covered and the time taken
The total distance covered by the train is given as 3584 km. The time taken is 2 days and 8 hours.

### Step 2: Convert the time into hours
1 day = 24 hours, so:
- 2 days = 2 * 24 = 48 hours
- 8 hours = 8 hours
- Total time = 48 + 8 = 56 hours

### Step 3: Calculate the average speed for the entire journey
Average speed is calculated using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
Substituting the values:
\[ \text{Average Speed} = \frac{3584 \text{ km}}{56 \text{ hours}} \]
Calculating this gives:
\[ \text{Average Speed} = 64 \text{ km/h} \]

### Step 4: Calculate the distance covered on each day
- Distance covered on the first day = 1440 km
- Distance covered on the second day = 1608 km

### Step 5: Calculate the remaining distance
Remaining distance = Total distance - Distance covered on first day - Distance covered on second day
\[ \text{Remaining Distance} = 3584 \text{ km} - 1440 \text{ km} - 1608 \text{ km} \]
Calculating this gives:
\[ \text{Remaining Distance} = 3584 - 1440 - 1608 = 536 \text{ km} \]

### Step 6: Calculate the time left for the remaining distance
The time taken for the first two days is 2 days (48 hours) + 8 hours = 56 hours. Since the entire journey is completed in 56 hours, there is no time left for the remaining distance.

### Step 7: Calculate the average speed for the remaining distance
Since the remaining distance is 536 km and the time taken is 8 hours (the remaining part of the journey):
\[ \text{Average Speed for Remaining Distance} = \frac{536 \text{ km}}{8 \text{ hours}} \]
Calculating this gives:
\[ \text{Average Speed for Remaining Distance} = 67 \text{ km/h} \]

### Step 8: Calculate the difference in average speeds
Now, we find the difference between the average speed for the remaining distance and the average speed for the entire journey:
\[ \text{Difference} = \text{Average Speed for Remaining Distance} - \text{Average Speed for Entire Journey} \]
Substituting the values:
\[ \text{Difference} = 67 \text{ km/h} - 64 \text{ km/h} = 3 \text{ km/h} \]

### Final Answer
The average speed of the train for the remaining part of the journey differs from that for the entire journey by **3 km/h**.

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