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Nomkhosi is a teacher in Smithfield and lives in Rouxville. She travels 39,2 km at an average speed of 80 km/h daily to work. It normally takes her approximately 29 minutes. Due to the road maintenance, she must add an extra 10 min for one stop and go on the road.

Mathematics

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Here are the solutions to Question 3:

3.1.1

  1. Calculate the daily distance traveled.

    Nomkhosi travels 39.2 km to work and 39.2 km back home.

    Daily distance=39.2 km×2=78.4 km\text{Daily distance} = 39.2 \text{ km} \times 2 = 78.4 \text{ km}
  2. Calculate the total weekly distance.

    Assuming a 5-day work week:

    Weekly distance=78.4 km/day×5 days/week=392 km\text{Weekly distance} = 78.4 \text{ km/day} \times 5 \text{ days/week} = 392 \text{ km}

    The total number of kilometers that she travels per week is 392 km\boxed{\text{392 km}}.

    3.1.2

  3. Calculate the total travel time to work (one way).

    Normal travel time = 29 minutes.
    Extra time due to road maintenance = 10 minutes.

    Total travel time=29 minutes+10 minutes=39 minutes\text{Total travel time} = 29 \text{ minutes} + 10 \text{ minutes} = 39 \text{ minutes}
  4. Convert the total travel time to hours.

    Since 1 hour = 60 minutes:

    Total travel time in hours=39 minutes60 minutes/hour=0.65 hours\text{Total travel time in hours} = \frac{39 \text{ minutes}}{60 \text{ minutes/hour}} = 0.65 \text{ hours}

    It takes Nomkhosi 0.65 hours\boxed{\text{0.65 hours}} to get to work due to Stop and go.

    3.1.3

  5. Determine the required arrival time at school.

    School starts at 07:30. Nomkhosi must be at school 10 minutes before school starts.

    Required arrival time=07:30−10 minutes=07:20\text{Required arrival time} = 07:30 - 10 \text{ minutes} = 07:20
  6. Determine the travel time to work in minutes.

    From 3.1.2, the total travel time to work (one way) is 39 minutes.

  7. Calculate the departure time from home.

    Departure time=Required arrival time−Travel time\text{Departure time} = \text{Required arrival time} - \text{Travel time} Departure time=07:20−39 minutes\text{Departure time} = 07:20 - 39 \text{ minutes}

    To subtract 39 minutes from 07:20:
    07:20 is 7 hours and 20 minutes.
    Subtract 20 minutes: 07:00. Remaining to subtract: 39−20=1939 - 20 = 19 minutes.
    Subtract 19 minutes from 07:00: 06:41.
    Nomkhosi must leave her home by 06:41\boxed{\text{06:41}}.

    3.2.1

  8. Determine the total volume of diluted juice.

    2 litres of Oros concentrate makes 8 litres of juice.

  9. Convert the total volume of juice to milliliters.

    Since 1 litre = 1000 milliliters:

    Total juice volume=8 litres×1000 ml/litre=8000 ml\text{Total juice volume} = 8 \text{ litres} \times 1000 \text{ ml/litre} = 8000 \text{ ml}
  10. Determine the volume of one cup.

    Given: 1 cup = 250 ml.

  11. Calculate the number of cups that can be served.

    Number of cups=Total juice volumeVolume per cup=8000 ml250 ml/cup=32 cups\text{Number of cups} = \frac{\text{Total juice volume}}{\text{Volume per cup}} = \frac{8000 \text{ ml}}{250 \text{ ml/cup}} = 32 \text{ cups}

    32 cups\boxed{\text{32 cups}} can be served from a 2-litre concentrate juice.

    3.2.2

  12. Calculate the total number of scones sold.

    Mrs. Marais sold 58 packets, and each packet had 5 scones.

    Total scones sold=58 packets×5 scones/packet=290 scones\text{Total scones sold} = 58 \text{ packets} \times 5 \text{ scones/packet} = 290 \text{ scones}
  13. Determine the amount of self-raising white flour per scone.

    The recipe uses 200 grams of self-raising white flour and "Serves 9 people". Assuming one serving is one scone, then one batch makes 9 scones.

    Flour per scone=200 grams9 scones\text{Flour per scone} = \frac{200 \text{ grams}}{9 \text{ scones}}
  14. Calculate the total amount of self-raising white flour used in grams.

    Total flour used=290 scones×200 grams9 scones=580009 grams≈6444.44 grams\text{Total flour used} = 290 \text{ scones} \times \frac{200 \text{ grams}}{9 \text{ scones}} = \frac{58000}{9} \text{ grams} \approx 6444.44 \text{ grams}
  15. Convert the total amount of flour from grams to kilograms.

    Since 1 kg = 1000 grams:

    Total flour used in kg=6444.44 grams1000 grams/kg≈6.44444 kg\text{Total flour used in kg} = \frac{6444.44 \text{ grams}}{1000 \text{ grams/kg}} \approx 6.44444 \text{ kg}

    Rounding to two decimal places:

    Total flour used in kg≈6.44 kg\text{Total flour used in kg} \approx 6.44 \text{ kg}

    Approximately 6.44 kg\boxed{\text{6.44 kg}} of self-raising white flour was used.

    3.2.3

  16. Identify the amount of butter from the recipe.

    The recipe uses 50 grams of butter.

  17. Convert the amount of butter from grams to kilograms.

    Since 1 kg = 1000 grams:

    Butter in kg=50 grams1000 grams/kg=0.05 kg\text{Butter in kg} = \frac{50 \text{ grams}}{1000 \text{ grams/kg}} = 0.05 \text{ kg}

    The amount of butter is 0.05 kg\boxed{\text{0.05 kg}}.

    3.2.4

  18. Identify the amounts of butter and self-raising flour from the recipe.

    Butter = 50 grams
    Self-raising white flour = 200 grams

  19. Write the ratio of butter to self-raising flour.

    Ratio=Butter:Flour=50 grams:200 grams\text{Ratio} = \text{Butter} : \text{Flour} = 50 \text{ grams} : 200 \text{ grams}
  20. Simplify the ratio.

    Divide both sides by the greatest common divisor, which is 50.

    5050:20050=1:4\frac{50}{50} : \frac{200}{50} = 1 : 4

    The ratio of butter to self-raising flour in simplified form is 1:4\boxed{1:4}.

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