Alright class, let's go through the steps to solve these questions in detail.
### 2.2.1 Determine the time taken to travel to Cape Town, without the 3 rest breaks that were made (in hours and minutes).
#### Step-by-Step Solution:
1. Identify Departure and Arrival Times:
- The family left home at 6:00 AM.
- They arrived at their destination at 23:20 (or 11:20 PM).
2. Convert These Times into Minutes Since Midnight:
- Departure time at 6:00 AM is [tex]\( 6 \times 60 = 360 \)[/tex] minutes since midnight.
- Arrival time at 23:20 is [tex]\( 23 \times 60 + 20 = 1400 \)[/tex] minutes since midnight.
3. Calculate the Total Travel Time in Minutes:
- Total travel time in minutes = Arrival time in minutes - Departure time in minutes
- Total travel time in minutes = 1400 - 360 = 1040 minutes
4. Account for the Rest Breaks:
- Each rest break is 1 hour (or 60 minutes) and there were 3 rest breaks.
- Total rest time = [tex]\( 3 \times 60 = 180 \)[/tex] minutes
5. Subtract the Rest Time from Total Travel Time:
- Effective travel time in minutes = Total travel time in minutes - Total rest time
- Effective travel time in minutes = 1040 - 180 = 860 minutes
6. Convert the Effective Travel Time into Hours and Minutes:
- Hours = [tex]\( \frac{860}{60} = 14 \)[/tex] hours (since 860 divided by 60 gives 14 as a quotient)
- Minutes = [tex]\( 860 \mod 60 = 20 \)[/tex] minutes (since 860 divided by 60 leaves a remainder of 20)
Thus, the time taken to travel to Cape Town, excluding the 3 rest breaks, is 14 hours and 20 minutes.
### 2.2.2 Calculate the Average Speed
#### Step-by-Step Solution:
1. Calculate the Total Distance Covered:
- Given that the total distance covered is 1420 km.
2. Use the Effective Travel Time from Step 2.2.1:
- Effective travel time is 14 hours and 20 minutes, which is 860 minutes in total.
- Convert this time back into hours for the speed calculation.
- Effective travel time in hours = [tex]\( \frac{860}{60} = 14.3333 \)[/tex] hours (since 860 divided by 60 is approximately 14.3333 hours)
3. Apply the Average Speed Formula:
- Average speed = [tex]\( \frac{\text{Distance}}{\text{Time}} \)[/tex]
- Average speed = [tex]\( \frac{1420 \text{ km}}{14.3333 \text{ hours}} \)[/tex]
4. Calculate the Result:
- Average speed ≈ 99.07 km/h
We round the result to two decimal places.
Therefore, the average speed at which they drove is 99.07 km/h.
