Answer :
Sure! Let's break down the problem step by step and find the average driving speed.
### Step 1: Recall the Information Needed
To calculate the average driving speed, we need:
1. The total distance traveled.
2. The total time spent driving (excluding any breaks).
### Step 2: Analyze the Given Information
From the problem, we have:
1. The total distance of the trip: [tex]\( 208 \)[/tex] kilometers.
2. The total time of the trip including the break: [tex]\( 2 \)[/tex] hours.
3. The duration of the break: [tex]\( 15 \)[/tex] minutes.
### Step 3: Convert Break Time to Hours
Since the break is given in minutes, we need to convert it to hours to match the time units.
[tex]\[ \text{Break time in hours} = \frac{15 \text{ minutes}}{60} = 0.25 \text{ hours} \][/tex]
### Step 4: Calculate the Actual Driving Time
To find the actual driving time, we subtract the break time from the total trip time:
[tex]\[ \text{Driving time} = \text{Total time} - \text{Break time} = 2 \text{ hours} - 0.25 \text{ hours} = 1.75 \text{ hours} \][/tex]
### Step 5: Calculate the Average Driving Speed
The formula for average speed is:
[tex]\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Actual driving time}} \][/tex]
Substituting the values we have:
[tex]\[ \text{Average speed} = \frac{208 \text{ km}}{1.75 \text{ hours}} \approx 118.857 \text{ kph} \][/tex]
### Conclusion: Finding the Closest Option
Among the given options:
A [tex]\( 104 \)[/tex] kph
B [tex]\( 112 \)[/tex] kph
C [tex]\( 119 \)[/tex] kph
D [tex]\( 193 \)[/tex] kph
The value [tex]\( 118.857 \)[/tex] kph is closest to [tex]\( 119 \)[/tex] kph.
### Final Answer
Therefore, the average driving speed was approximately [tex]\( \boxed{119} \)[/tex] kph.
### Step 1: Recall the Information Needed
To calculate the average driving speed, we need:
1. The total distance traveled.
2. The total time spent driving (excluding any breaks).
### Step 2: Analyze the Given Information
From the problem, we have:
1. The total distance of the trip: [tex]\( 208 \)[/tex] kilometers.
2. The total time of the trip including the break: [tex]\( 2 \)[/tex] hours.
3. The duration of the break: [tex]\( 15 \)[/tex] minutes.
### Step 3: Convert Break Time to Hours
Since the break is given in minutes, we need to convert it to hours to match the time units.
[tex]\[ \text{Break time in hours} = \frac{15 \text{ minutes}}{60} = 0.25 \text{ hours} \][/tex]
### Step 4: Calculate the Actual Driving Time
To find the actual driving time, we subtract the break time from the total trip time:
[tex]\[ \text{Driving time} = \text{Total time} - \text{Break time} = 2 \text{ hours} - 0.25 \text{ hours} = 1.75 \text{ hours} \][/tex]
### Step 5: Calculate the Average Driving Speed
The formula for average speed is:
[tex]\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Actual driving time}} \][/tex]
Substituting the values we have:
[tex]\[ \text{Average speed} = \frac{208 \text{ km}}{1.75 \text{ hours}} \approx 118.857 \text{ kph} \][/tex]
### Conclusion: Finding the Closest Option
Among the given options:
A [tex]\( 104 \)[/tex] kph
B [tex]\( 112 \)[/tex] kph
C [tex]\( 119 \)[/tex] kph
D [tex]\( 193 \)[/tex] kph
The value [tex]\( 118.857 \)[/tex] kph is closest to [tex]\( 119 \)[/tex] kph.
### Final Answer
Therefore, the average driving speed was approximately [tex]\( \boxed{119} \)[/tex] kph.
