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Siphiwe and Matete are travelling from Pretoria to the Kruger Park which is 3 km from Hazyview. They are driving at the speed of 120 km/h. They left Pretoria at 01h30 and had to rest for 10 minutes after every 100 km drive.

Mathematics

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Answers

3 parts
b(i)

558 km558 \text{ km}

b(ii)

300 km300 \text{ km}

258 km258 \text{ km}

b(iii)

06h3906\text{h}39

Step-by-step solution

9 steps

Part b(i)· 2 steps

  1. Identify the distances between each point on the journey from Pretoria to Kruger Park.

    The distances are:
    Pretoria to Witbank: 120 km120 \text{ km}
    Witbank to Lydenburg: 280 km280 \text{ km}
    Lydenburg to Whiteriver: 140 km140 \text{ km}
    Whiteriver to Hazyview: 15 km15 \text{ km}
    Hazyview to Kruger Park: 3 km3 \text{ km}

  2. Sum all the distances to find the total distance.

    Total distance=120 km+280 km+140 km+15 km+3 km\text{Total distance} = 120 \text{ km} + 280 \text{ km} + 140 \text{ km} + 15 \text{ km} + 3 \text{ km} Total distance=558 km\text{Total distance} = 558 \text{ km}

    The total distance by road from Pretoria to the Kruger Park is 558 km\boxed{558 \text{ km}}.

Part b(ii)

300 km300 \text{ km}

  1. Determine the total distance of the journey.

    From part (i), the total distance is 558 km558 \text{ km}.

  2. Allocate driving segments of 100 km100 \text{ km} alternately, starting with Siphiwe.

    Siphiwe drives the 1st 100 km100 \text{ km}.
    Matete drives the 2nd 100 km100 \text{ km}.
    Siphiwe drives the 3rd 100 km100 \text{ km}.
    Matete drives the 4th 100 km100 \text{ km}.
    Siphiwe drives the 5th 100 km100 \text{ km}.
    Remaining distance = 558 km−(5×100 km)=558 km−500 km=58 km558 \text{ km} - (5 \times 100 \text{ km}) = 558 \text{ km} - 500 \text{ km} = 58 \text{ km}.
    Matete drives the remaining 58 km58 \text{ km}.

  3. Calculate the total kilometres driven by each person.

    Siphiwe's total distance = 100 km+100 km+100 km=300 km100 \text{ km} + 100 \text{ km} + 100 \text{ km} = 300 \text{ km}.
    Matete's total distance = 100 km+100 km+58 km=258 km100 \text{ km} + 100 \text{ km} + 58 \text{ km} = 258 \text{ km}.
    Siphiwe drives 300 km\boxed{300 \text{ km}} and Matete drives 258 km\boxed{258 \text{ km}}.

Part b(iii)

06h3906\text{h}39

  1. Calculate the driving time.

    Total distance = 558 km558 \text{ km} (from part i).
    Average speed = 120 km/h120 \text{ km/h}.

    Driving time=DistanceSpeed=558 km120 km/h=4.65 hours\text{Driving time} = \frac{\text{Distance}}{\text{Speed}} = \frac{558 \text{ km}}{120 \text{ km/h}} = 4.65 \text{ hours}
  2. Convert the driving time to hours and minutes.

    0.65 hours×60 minutes/hour=39 minutes0.65 \text{ hours} \times 60 \text{ minutes/hour} = 39 \text{ minutes}.
    So, the driving time is 4 hours and 39 minutes4 \text{ hours and } 39 \text{ minutes}.

  3. Add the rest time to the driving time.

    The problem states they stop once for 30 minutes30 \text{ minutes} to rest.

    Total time spent travelling=4 hours 39 minutes+30 minutes\text{Total time spent travelling} = 4 \text{ hours } 39 \text{ minutes} + 30 \text{ minutes} Total time spent travelling=4 hours 69 minutes\text{Total time spent travelling} = 4 \text{ hours } 69 \text{ minutes}

    Since 69 minutes=1 hour and 9 minutes69 \text{ minutes} = 1 \text{ hour and } 9 \text{ minutes}:

    Total time spent travelling=4 hours+1 hour 9 minutes=5 hours and 9 minutes\text{Total time spent travelling} = 4 \text{ hours} + 1 \text{ hour } 9 \text{ minutes} = 5 \text{ hours and } 9 \text{ minutes}
  4. Calculate the arrival time by adding the total travel time to the departure time.

    Departure time = 01h3001\text{h}30.

    Arrival time=01h30+5h09=06h39\text{Arrival time} = 01\text{h}30 + 5\text{h}09 = 06\text{h}39

    They reach the Kruger Park at 06h39\boxed{06\text{h}39}.

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