Calculating Average Speed of a Train

To find the average speed of the train, we need to calculate the total distance covered by the train and the total time taken for the entire journey. The average speed is then calculated by dividing the total distance by the total time.

The formula for average speed is:

\( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \)

Understanding the Train's Journey Segments

The train's journey is described in three distinct parts:

• Part 1: Speed = 28 kmph, Time = 4 hours
• Part 2: Speed = 30 kmph, Time = 5 hours
• Part 3: Distance = 40 km, Time = 1 hour

Calculating Total Distance Covered by the Train

First, let's find the distance covered in the first two parts of the journey. The distance covered is calculated as Speed × Time.

• Distance in Part 1 = \( 28 \text{ kmph} \times 4 \text{ hours} = 112 \text{ km} \)
• Distance in Part 2 = \( 30 \text{ kmph} \times 5 \text{ hours} = 150 \text{ km} \)
• Distance in Part 3 = \( 40 \text{ km} \) (This is given directly)

Now, we sum up the distances from all three parts to get the total distance.

\( \text{Total Distance} = \text{Distance in Part 1} + \text{Distance in Part 2} + \text{Distance in Part 3} \)

\( \text{Total Distance} = 112 \text{ km} + 150 \text{ km} + 40 \text{ km} \)

\( \text{Total Distance} = 302 \text{ km} \)

Calculating Total Time Taken for the Journey

The total time taken is the sum of the time taken for each part of the journey.

• Time in Part 1 = 4 hours
• Time in Part 2 = 5 hours
• Time in Part 3 = 1 hour

\( \text{Total Time} = \text{Time in Part 1} + \text{Time in Part 2} + \text{Time in Part 3} \)

\( \text{Total Time} = 4 \text{ hours} + 5 \text{ hours} + 1 \text{ hour} \)

\( \text{Total Time} = 10 \text{ hours} \)

Finding the Average Speed per Hour

Finally, we can calculate the average speed using the total distance and total time.

\( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \)

\( \text{Average Speed} = \frac{302 \text{ km}}{10 \text{ hours}} \)

\( \text{Average Speed} = 30.2 \text{ kmph} \)

The average speed of the train per hour is 30.2 kmph.