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
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.

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Answer

392 km

Here are the solutions to Question 3:

3.1.1 Step 1: Calculate the daily distance traveled. Nomkhosi travels 39.2 km to work and 39.2 km back home. Dailydistance=39.2km×2=78.4kmDaily distance = 39.2 km \times 2 = 78.4 km

Step 2: Calculate the total weekly distance. Assuming a 5-day work week: Weeklydistance=78.4km/day×5days/week=392kmWeekly distance = 78.4 km/day \times 5 days/week = 392 km The total number of kilometers that she travels per week is 392km\boxed{392 km}.

3.1.2 Step 1: Calculate the total travel time to work (one way). Normal travel time = 29 minutes. Extra time due to road maintenance = 10 minutes. Totaltraveltime=29minutes+10minutes=39minutesTotal travel time = 29 minutes + 10 minutes = 39 minutes

Step 2: Convert the total travel time to hours. Since 1 hour = 60 minutes: Totaltraveltimeinhours=39minutes60minutes/hour=0.65hoursTotal travel time in hours = \frac{39 minutes}{60 minutes/hour} = 0.65 hours It takes Nomkhosi 0.65hours\boxed{0.65 hours} to get to work due to Stop and go.

3.1.3 Step 1: Determine the required arrival time at school. School starts at 07:30. Nomkhosi must be at school 10 minutes before school starts. Requiredarrivaltime=07:3010minutes=07:20Required arrival time = 07:30 - 10 minutes = 07:20

Step 2: Determine the travel time to work in minutes. From 3.1.2, the total travel time to work (one way) is 39 minutes.

Step 3: Calculate the departure time from home. Departuretime=RequiredarrivaltimeTraveltimeDeparture time = Required arrival time - Travel time Departuretime=07:2039minutesDeparture time = 07:20 - 39 minutes To subtract 39 minutes from 07:20: 07:20 is 7 hours and 20 minutes. Subtract 20 minutes: 07:00. Remaining to subtract: 3920=1939 - 20 = 19 minutes. Subtract 19 minutes from 07:00: 06:41. Nomkhosi must leave her home by 06:41\boxed{06:41}.

3.2.1 Step 1: Determine the total volume of diluted juice. 2 litres of Oros concentrate makes 8 litres of juice.

Step 2: Convert the total volume of juice to milliliters. Since 1 litre = 1000 milliliters: Totaljuicevolume=8litres×1000ml/litre=8000mlTotal juice volume = 8 litres \times 1000 ml/litre = 8000 ml

Step 3: Determine the volume of one cup. Given: 1 cup = 250 ml.

Step 4: Calculate the number of cups that can be served. Numberofcups=TotaljuicevolumeVolumepercup=8000ml250ml/cup=32cupsNumber of cups = \frac{Total juice volume}{Volume per cup} = \frac{8000 ml}{250 ml/cup} = 32 cups 32cups\boxed{32 cups} can be served from a 2-litre concentrate juice.

3.2.2 Step 1: Calculate the total number of scones sold. Mrs. Marais sold 58 packets, and each packet had 5 scones. Totalsconessold=58packets×5scones/packet=290sconesTotal scones sold = 58 packets \times 5 scones/packet = 290 scones

Step 2: 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. Flourperscone=200grams9sconesFlour per scone = \frac{200 grams}{9 scones}

Step 3: Calculate the total amount of self-raising white flour used in grams. Totalflourused=290scones×200grams9scones=580009grams6444.44gramsTotal flour used = 290 scones \times \frac{200 grams}{9 scones} = \frac{58000}{9} grams \approx 6444.44 grams

Step 4: Convert the total amount of flour from grams to kilograms. Since 1 kg = 1000 grams: Totalflourusedinkg=6444.44grams1000grams/kg6.44444kgTotal flour used in kg = \frac{6444.44 grams}{1000 grams/kg} \approx 6.44444 kg Rounding to two decimal places: Totalflourusedinkg6.44kgTotal flour used in kg \approx 6.44 kg Approximately 6.44kg\boxed{6.44 kg} of self-raising white flour was used.

3.2.3 Step 1: Identify the amount of butter from the recipe. The recipe uses 50 grams of butter.

Step 2: Convert the amount of butter from grams to kilograms. Since 1 kg = 1000 grams: Butterinkg=50grams1000grams/kg=0.05kgButter in kg = \frac{50 grams}{1000 grams/kg} = 0.05 kg The amount of butter is 0.05kg\boxed{0.05 kg}.

3.2.4 Step 1: Identify the amounts of butter and self-raising flour from the recipe. Butter = 50 grams Self-raising white flour = 200 grams

Step 2: Write the ratio of butter to self-raising flour. Ratio=Butter:Flour=50grams:200gramsRatio = Butter : Flour = 50 grams : 200 grams

Step 3: 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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Quick Answer

3.1.1 Step 1: Calculate the daily distance traveled. Nomkhosi travels 39.2 km to work and 39.2 km back home.

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

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Here are the solutions to Question 3: 3.1.1 Step 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 Step 2: Calculate the total weekly distance. Assuming a 5-day work week: Weekly distance = 78.4 km/day × 5 days/week = 392 km The total number of kilometers that she travels per week is 392 km. 3.1.2 Step 1: 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 Step 2: Convert the total travel time to hours. Since 1 hour = 60 minutes: Total travel time in hours = 39 minutes60 minutes/hour = 0.65 hours It takes Nomkhosi 0.65 hours to get to work due to Stop and go. 3.1.3 Step 1: 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 Step 2: Determine the travel time to work in minutes. From 3.1.2, the total travel time to work (one way) is 39 minutes. Step 3: Calculate the departure time from home. Departure time = Required arrival time - Travel time Departure time = 07:20 - 39 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 = 19 minutes. Subtract 19 minutes from 07:00: 06:41. Nomkhosi must leave her home by 06:41. 3.2.1 Step 1: Determine the total volume of diluted juice. 2 litres of Oros concentrate makes 8 litres of juice. Step 2: Convert the total volume of juice to milliliters. Since 1 litre = 1000 milliliters: Total juice volume = 8 litres × 1000 ml/litre = 8000 ml Step 3: Determine the volume of one cup. Given: 1 cup = 250 ml. Step 4: Calculate the number of cups that can be served. Number of cups = Total juice volumeVolume per cup = 8000 ml250 ml/cup = 32 cups 32 cups can be served from a 2-litre concentrate juice. 3.2.2 Step 1: 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 Step 2: 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 Step 3: Calculate the total amount of self-raising white flour used in grams. Total flour used = 290 scones × 200 grams9 scones = (58000)/(9) grams ≈ 6444.44 grams Step 4: 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 Rounding to two decimal places: Total flour used in kg ≈ 6.44 kg Approximately 6.44 kg of self-raising white flour was used. 3.2.3 Step 1: Identify the amount of butter from the recipe. The recipe uses 50 grams of butter. Step 2: Convert the amount of butter from grams to kilograms. Since 1 kg = 1000 grams: Butter in kg = 50 grams1000 grams/kg = 0.05 kg The amount of butter is 0.05 kg. 3.2.4 Step 1: Identify the amounts of butter and self-raising flour from the recipe. Butter = 50 grams Self-raising white flour = 200 grams Step 2: Write the ratio of butter to self-raising flour. Ratio = Butter : Flour = 50 grams : 200 grams Step 3: Simplify the ratio. Divide both sides by the greatest common divisor, which is 50. (50)/(50) : (200)/(50) = 1 : 4 The ratio of butter to self-raising flour in simplified form is 1:4. 3 done, 2 left today. You're making progress.