Certainly! Let's break down this problem step-by-step.
### Step 1: Define Given Information
1. Total Distance of Journey: [tex]\( 900 \, \text{km} \)[/tex]
2. Distance Travelled in October: [tex]\( 120 \, \text{km} \)[/tex]
3. Average Speed for Entire Journey: [tex]\( 60 \, \text{km/h} \)[/tex]
### Step 2: Calculate Total Time for Journey
To find the total time taken for the entire journey, use the formula:
[tex]\[ \text{Total Time} = \frac{\text{Total Distance}}{\text{Average Speed}} \][/tex]
Given:
[tex]\[ \text{Total Distance} = 900 \, \text{km} \][/tex]
[tex]\[ \text{Average Speed} = 60 \, \text{km/h} \][/tex]
Substituting the values:
[tex]\[ \text{Total Time} = \frac{900 \, \text{km}}{60 \, \text{km/h}} = 15 \, \text{hours} \][/tex]
### Step 3: Calculate Time for October Segment
Next, to find the time taken for the October segment, use the formula:
[tex]\[ \text{Time for October Segment} = \frac{\text{Distance Travelled in October}}{\text{Average Speed}} \][/tex]
Given:
[tex]\[ \text{Distance Travelled in October} = 120 \, \text{km} \][/tex]
[tex]\[ \text{Average Speed} = 60 \, \text{km/h} \][/tex]
Substituting the values:
[tex]\[ \text{Time for October Segment} = \frac{120 \, \text{km}}{60 \, \text{km/h}} = 2 \, \text{hours} \][/tex]
### Summary of Results
- Total Time for Entire Journey: [tex]\( 15 \, \text{hours} \)[/tex]
- Time for October Segment: [tex]\( 2 \, \text{hours} \)[/tex]
So, the journey will take a total of 15 hours, and specifically, the October segment of the journey (120 km) will take 2 hours.
