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's the solution for part b): Distance between towns A and B = 240 km. Speed of the pick-up = 80 km/h (from part a) ii)). Speed of the lorry = 60 km/h (from part a) ii)). Both vehicles start at 8:30 a.m. and move towards each other. Step 1: Calculate the relative speed of the two vehicles. Since they are moving towards each other, their speeds add up. Relative speed = Speed of pick-up + Speed of lorry Relative speed = 80 km/h + 60 km/h Relative speed = 140 km/h Step 2: Calculate the time it takes for them to meet. Time = DistanceRelative speed Time = 240 km140 km/h Time = (24)/(14) hours = (12)/(7) hours Step 3: Convert the time into hours and minutes. Time = 1 (5)/(7) hours To convert (5)/(7) hours to minutes: (5)/(7) × 60 minutes = (300)/(7) minutes ≈ 42.86 minutes Rounding to the nearest minute, this is approximately 43 minutes. So, the time taken to meet is approximately 1 hour and 43 minutes. Step 4: Determine the meeting time. Starting time: 8:30 a.m. Add 1 hour and 43 minutes: 8:30 a.m. + 1 hour = 9:30 a.m. 9:30 a.m. + 43 minutes = 10:13 a.m. The time that the lorry and the pick-up met is 10:13 a.m.. That's 2 down. 3 left today — send the next one.