A train travels with a speed of 20 m/s in the first 10 minutes, goes 8.5 km in the next 10 minutes, 11 km in the next 10,8.5 km in the next 10 and 6 km in the next 10 minutes. What is the average speed of the train in kilometer per hour for the journey described?

Options

A. 42 kmph
B. 35.8 kmph
C. 55.2 kmph
D. 46 kmph

Answer

To find the average speed of the train for the entire journey, we will follow these steps:

### Step 1: Calculate the distance covered in the first segment
The train travels at a speed of 20 m/s for the first 10 minutes.

1. Convert 10 minutes to seconds:
\[ 10 \text{ minutes} = 10 \times 60 = 600 \text{ seconds} \]

2. Calculate the distance using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 20 \text{ m/s} \times 600 \text{ seconds} = 12000 \text{ meters} \]

3. Convert meters to kilometers:
\[ 12000 \text{ meters} = \frac{12000}{1000} = 12 \text{ km} \]

### Step 2: Calculate the total distance covered in subsequent segments
The distances covered in the next segments are as follows:
- 8.5 km in the next 10 minutes
- 11 km in the next 10 minutes
- 8.5 km in the next 10 minutes
- 6 km in the next 10 minutes

Now, sum these distances:
\[ \text{Total distance} = 12 \text{ km} + 8.5 \text{ km} + 11 \text{ km} + 8.5 \text{ km} + 6 \text{ km} \]
Calculating this:
\[ 12 + 8.5 + 11 + 8.5 + 6 = 46 \text{ km} \]

### Step 3: Calculate the total time taken
The total time for the journey is:
- 10 minutes for the first segment
- 10 minutes for the second segment
- 10 minutes for the third segment
- 10 minutes for the fourth segment
- 10 minutes for the fifth segment

Total time:
\[ 10 + 10 + 10 + 10 + 10 = 50 \text{ minutes} \]

Convert minutes to hours:
\[ 50 \text{ minutes} = \frac{50}{60} \text{ hours} = \frac{5}{6} \text{ hours} \]

### Step 4: Calculate the average speed
Average speed is calculated using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
Substituting the values we have:
\[ \text{Average Speed} = \frac{46 \text{ km}}{\frac{5}{6} \text{ hours}} = 46 \times \frac{6}{5} \]
Calculating this:
\[ 46 \times \frac{6}{5} = \frac{276}{5} = 55.2 \text{ km/h} \]

### Final Answer
Thus, the average speed of the train is:
\[ \text{Average Speed} = 55.2 \text{ km/h} \]

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