A tourist departs from Durban at 08:15 and drives to Kokstad via the N2. The total distance is 195 km. The vehicle maintains an average speed of 105 km/h. The traveller stops for a 20-minute coffee break in Port Shepstone. Determine the arrival time in Kokstad.

Mathematics
A tourist departs from Durban at 08:15 and drives to Kokstad via the N2. The total distance is 195 km. The vehicle maintains an average speed of 105 km/h. The traveller stops for a 20-minute coffee break in Port Shepstone. Determine the arrival time in Kokstad.

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Answer

Cannot be answered without Annexure A (the map).

Step 1: Address question 2.1.1. The question asks to use a map (Annexure A) to describe the position of Maseru relative to Matatiele. Since Annexure A is not provided, this question cannot be answered. Cannot be answered without Annexure A (the map).\text{Cannot be answered without Annexure A (the map).}

Step 2: Verify the map scale for 2.1.2. Given: Map distance = 14 mm Actual road distance = 35 km Claimed map scale = 1 : 500 000

First, convert the actual road distance to millimetres to match the map distance unit. 1km=1000m1 km = 1000 m 1m=1000mm1 m = 1000 mm 1km=1000×1000mm=1,000,000mm1 km = 1000 \times 1000 mm = 1,000,000 mm So, 35km=35×1,000,000mm=35,000,000mm35 km = 35 \times 1,000,000 mm = 35,000,000 mm Now, calculate the actual map scale based on the given measurements: Mapscale=Mapdistance:ActualdistanceMap scale = Map distance : Actual distance Mapscale=14mm:35,000,000mmMap scale = 14 mm : 35,000,000 mm To express this as a ratio with 1 on the left side, divide both sides by 14: Mapscale=1414:35,000,00014Map scale = \frac{14}{14} : \frac{35,000,000}{14} Mapscale=1:2,500,000Map scale = 1 : 2,500,000 Compare this calculated scale to the traveler's claim: Calculated scale: 1 : 2,500,000 Claimed scale: 1 : 500,000 Since 2,500,000500,0002,500,000 \neq 500,000, the traveler's claim is incorrect. The traveler’s claim is incorrect. The calculated map scale is 1 : 2,500,000.\text{The traveler's claim is incorrect. The calculated map scale is 1 : 2,500,000.}

Step 3: Calculate the driving time for 2.1.3. Given: Total distance = 195 km Average speed = 105 km/h The formula for time is Time=DistanceSpeed\text{Time} = \frac{Distance}{Speed}. Drivingtime=195km105km/h1.8571hoursDriving time = \frac{195 km}{105 km/h} \approx 1.8571 hours Convert the decimal part of the hour to minutes: 0.8571hours×60minutes/hour51.426minutes0.8571 hours \times 60 minutes/hour \approx 51.426 minutes Rounding to the nearest minute, the driving time is 1 hour and 51 minutes.

Step 4: Calculate the total travel time for 2.1.3. The traveler stops for a 20-minute coffee break. Totaltraveltime=Drivingtime+CoffeebreaktimeTotal travel time = Driving time + Coffee break time Totaltraveltime=1hour51minutes+20minutesTotal travel time = 1 hour 51 minutes + 20 minutes Totaltraveltime=1hour71minutesTotal travel time = 1 hour 71 minutes Since 71 minutes is 1 hour and 11 minutes: Totaltraveltime=1hour+1hour11minutes=2hours11minutesTotal travel time = 1 hour + 1 hour 11 minutes = 2 hours 11 minutes

Step 5: Determine the arrival time in Kokstad for 2.1.3. Departure time = 08:15 Add the total travel time: Arrivaltime=08:15+2hours11minutesArrival time = 08:15 + 2 hours 11 minutes Arrivaltime=10:26Arrival time = 10:26 Arrival time: 10:26\text{Arrival time: 10:26} Last free one today — make it count tomorrow, or type /upgrade for unlimited.

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Quick Answer

Address question 2.1.1. The question asks to use a map (Annexure A) to describe the position of Maseru relative to Matatiele.

A tourist departs from Durban at 08:15 and drives to Kokstad via the N2. The total distance is 195 km. The vehicle maintains an average speed of 105 km/h. The traveller stops for a 20-minute coffee break in Port Shepstone. Determine the arrival time in Kokstad.
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
Step 1: Address question 2.1.1. The question asks to use a map (Annexure A) to describe the position of Maseru relative to Matatiele. Since Annexure A is not provided, this question cannot be answered. Cannot be answered without Annexure A (the map). Step 2: Verify the map scale for 2.1.2. Given: Map distance = 14 mm Actual road distance = 35 km Claimed map scale = 1 : 500 000 First, convert the actual road distance to millimetres to match the map distance unit. 1 km = 1000 m 1 m = 1000 mm 1 km = 1000 × 1000 mm = 1,000,000 mm So, 35 km = 35 × 1,000,000 mm = 35,000,000 mm Now, calculate the actual map scale based on the given measurements: Map scale = Map distance : Actual distance Map scale = 14 mm : 35,000,000 mm To express this as a ratio with 1 on the left side, divide both sides by 14: Map scale = (14)/(14) : (35,000,000)/(14) Map scale = 1 : 2,500,000 Compare this calculated scale to the traveler's claim: Calculated scale: 1 : 2,500,000 Claimed scale: 1 : 500,000 Since 2,500,000 ≠ 500,000, the traveler's claim is incorrect. The traveler's claim is incorrect. The calculated map scale is 1 : 2,500,000. Step 3: Calculate the driving time for 2.1.3. Given: Total distance = 195 km Average speed = 105 km/h The formula for time is Time = DistanceSpeed. Driving time = 195 km105 km/h ≈ 1.8571 hours Convert the decimal part of the hour to minutes: 0.8571 hours × 60 minutes/hour ≈ 51.426 minutes Rounding to the nearest minute, the driving time is 1 hour and 51 minutes. Step 4: Calculate the total travel time for 2.1.3. The traveler stops for a 20-minute coffee break. Total travel time = Driving time + Coffee break time Total travel time = 1 hour 51 minutes + 20 minutes Total travel time = 1 hour 71 minutes Since 71 minutes is 1 hour and 11 minutes: Total travel time = 1 hour + 1 hour 11 minutes = 2 hours 11 minutes Step 5: Determine the arrival time in Kokstad for 2.1.3. Departure time = 08:15 Add the total travel time: Arrival time = 08:15 + 2 hours 11 minutes Arrival time = 10:26 Arrival time: 10:26 Last free one today — make it count tomorrow, or type /upgrade for unlimited.