Average Speed Calculation for Train Journey

This problem requires us to find the average speed of the train over its entire journey. The average speed is calculated by dividing the total distance covered by the total time taken.

Understanding the Formula

The formula for average speed is:

$$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $$

We need to ensure that the units are consistent. Since the distances are given in kilometers (km) and the required speed is in kilometers per hour (km/h), we need to convert the time from minutes to hours.

Step-by-Step Calculation

1. Calculate Total Distance

The train covers the journey in three parts. Let's sum the distances:

• Part 1 Distance: 40 km
• Part 2 Distance: 30 km
• Part 3 Distance: 20 km

Total Distance = 40 km + 30 km + 20 km = 90 km.

2. Calculate Total Time and Convert to Hours

The times taken for each part are:

• Part 1 Time: 45 minutes
• Part 2 Time: 30 minutes
• Part 3 Time: 15 minutes

Total Time in minutes = 45 + 30 + 15 = 90 minutes.

To convert minutes to hours, we divide by 60 (since there are 60 minutes in an hour):

$$ \text{Total Time in hours} = \frac{90 \text{ minutes}}{60 \text{ minutes/hour}} = 1.5 \text{ hours} $$

3. Calculate Average Speed

Now we can use the average speed formula with the total distance and total time in hours:

$$ \text{Average Speed} = \frac{90 \text{ km}}{1.5 \text{ hours}} $$

$$ \text{Average Speed} = 60 \text{ km/h} $$

Conclusion

The average speed of the train for the whole journey is 60 km/h.