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.