Calculating Average Speed of a Bus

The problem asks us to find the average speed of a bus that travels in two distinct stages. To find the average speed, we need to determine the total distance traveled by the bus and the total time taken for the journey.

The formula for average speed is:

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

Analyzing the Bus Journey - Stage by Stage

The bus journey is described in two parts:

1. The first part covers a certain distance in a given time.
2. The second part covers a certain time at a given speed, from which we can calculate the distance.

Stage 1: First part of the journey

• Distance traveled (\(\text{D}_1\)) = 150 Km
• Time taken (\(\text{T}_1\)) = 3 hours

In this stage, the distance and time are directly provided.

Stage 2: Next part of the journey

• Time taken (\(\text{T}_2\)) = 2 hours
• Speed during this stage (\(\text{S}_2\)) = 60 Km/hr

To find the distance traveled in this stage (\(\text{D}_2\)), we can use the formula: Distance = Speed \(\times\) Time.

$$ \text{D}_2 = \text{S}_2 \times \text{T}_2 $$

Substituting the given values:

$$ \text{D}_2 = 60 \, \text{Km/hr} \times 2 \, \text{hours} $$

$$ \text{D}_2 = 120 \, \text{Km} $$

Calculating Total Distance and Total Time

Now, we need to find the total distance covered and the total time taken for the entire journey.

• Total Distance (\(\text{D}_{\text{total}}\)) = Distance in Stage 1 + Distance in Stage 2
• Total Time (\(\text{T}_{\text{total}}\)) = Time in Stage 1 + Time in Stage 2

Calculating Total Distance:

$$ \text{D}_{\text{total}} = \text{D}_1 + \text{D}_2 $$

$$ \text{D}_{\text{total}} = 150 \, \text{Km} + 120 \, \text{Km} $$

$$ \text{D}_{\text{total}} = 270 \, \text{Km} $$

Calculating Total Time:

$$ \text{T}_{\text{total}} = \text{T}_1 + \text{T}_2 $$

$$ \text{T}_{\text{total}} = 3 \, \text{hours} + 2 \, \text{hours} $$

$$ \text{T}_{\text{total}} = 5 \, \text{hours} $$

Calculating the Average Speed

Using the total distance and total time, we can now calculate the average speed of the bus.

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

$$ \text{Average Speed} = \frac{270 \, \text{Km}}{5 \, \text{hours}} $$

$$ \text{Average Speed} = 54 \, \text{Km/hr} $$

Summary of Calculations

The calculated average speed of the bus is 54 Km/hr.

Revision Table: Average Speed Concepts

Additional Information: Understanding Average Speed in Travel

Average speed gives us an overall idea of how fast the bus traveled over the entire journey, considering periods of different speeds (or even stops, though none were mentioned here). It's not simply the average of the speeds during different segments, especially if the time or distance covered in each segment varies.

In this problem, the speed in the first stage was 150 Km / 3 hours = 50 Km/hr, and in the second stage, it was 60 Km/hr. The average speed (54 Km/hr) is a value between these two speeds. This is because the bus spent more time traveling at the lower speed (3 hours at 50 km/hr) than at the higher speed (2 hours at 60 km/hr), influencing the average towards the lower speed side.

Calculating average speed requires finding the total distance and dividing it by the total time, irrespective of how many segments the journey is broken into or how the speed varies within those segments.