A train covers the distance 200 meters 500 and 900 min 1 min, 2 minutes and 3 minutes respectively. In how many time it covers the distance of 2 km if it covers the distance every minute in the same order?

Options

A. 4 minutes
B. `4(1)/2`
C. 5 min
D. `5(1)/2` min

Answer

To solve the problem step by step, we will analyze the distances covered by the train in each minute and then determine how long it will take to cover 2 kilometers (2000 meters) following the same pattern.

### Step 1: Identify the distances and times
The train covers the following distances in the specified times:
- In 1 minute, it covers 200 meters.
- In 2 minutes, it covers 500 meters.
- In 3 minutes, it covers 900 meters.

### Step 2: Calculate the speeds for each segment
We can calculate the speed for each segment:
- Speed for the first minute (S1):
\[ S1 = \frac{D1}{T1} = \frac{200 \text{ meters}}{1 \text{ minute}} = 200 \text{ meters/minute} \]

- Speed for the second minute (S2):
\[ S2 = \frac{D2}{T2} = \frac{500 \text{ meters}}{2 \text{ minutes}} = 250 \text{ meters/minute} \]

- Speed for the third minute (S3):
\[ S3 = \frac{D3}{T3} = \frac{900 \text{ meters}}{3 \text{ minutes}} = 300 \text{ meters/minute} \]

### Step 3: Determine the pattern of speeds
The pattern of speeds is:
- 1st minute: 200 meters/minute
- 2nd minute: 250 meters/minute
- 3rd minute: 300 meters/minute
- 4th minute: We can assume the next speed will be 400 meters/minute (increasing by 100 meters/minute).

### Step 4: Calculate the total distance covered in a cycle
In one complete cycle (3 minutes), the total distance covered is:
\[ \text{Total distance in 3 minutes} = 200 + 500 + 900 = 1600 \text{ meters} \]

### Step 5: Calculate the distance covered in the next minute
In the 4th minute, the distance covered is:
\[ D4 = 400 \text{ meters} \]

### Step 6: Calculate the total distance covered in 4 minutes
After 4 minutes, the total distance covered is:
\[ \text{Total distance in 4 minutes} = 200 + 500 + 900 + 400 = 2000 \text{ meters} \]

### Step 7: Conclusion
The train covers a total distance of 2000 meters (or 2 kilometers) in 4 minutes.

### Final Answer
The train covers the distance of 2 kilometers in **4 minutes**.

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