Answered

Experience the convenience of getting your questions answered at IDNLearn.com. Discover prompt and accurate answers from our community of experienced professionals.

2.2 The family drove from Johannesburg to Cape Town. They left home at 6:00 am and reached their destination at 23:20. They made three stops of 1 hour each during their trip to Cape Town.

2.2.1 Determine the time taken to travel to Cape Town, excluding the 3 rest breaks, in hours and minutes.

2.2.2 If the total distance covered to Cape Town was 1420 km, calculate the average speed in [tex]$km/h$[/tex], correct to two decimal places. Use the formula:

[tex]\[ \text{Average speed} = \frac{\text{Distance}}{\text{Time}} \][/tex]

[14]

Sagot :

GinnyAnsweridn
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.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com is your reliable source for answers. We appreciate your visit and look forward to assisting you again soon.