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 the problems: 13. Two towns are 60 km apart. James leaves Town A at 8.00 a.m. travelling at 20 km/h. Peter leaves Town B at 9.00 a.m. travelling at 30 km/h towards James. a) How long after 8.00 a.m. do they meet? Step 1: Calculate the distance James travels from 8:00 a.m. to 9:00 a.m. Distance covered by James = Speed × Time = 20 km/h × 1 h = 20 km Step 2: Calculate the remaining distance between the towns at 9:00 a.m. Remaining distance = Total distance - Distance covered by James = 60 km - 20 km = 40 km Step 3: Calculate their relative speed since they are moving towards each other. Relative speed = James's speed + Peter's speed = 20 km/h + 30 km/h = 50 km/h Step 4: Calculate the time it takes for them to meet after 9:00 a.m. Time to meet = Remaining distanceRelative speed = 40 km50 km/h = 0.8 hours Step 5: Convert the time to minutes. 0.8 hours × 60 minutes/hour = 48 minutes Step 6: Calculate the total time after 8:00 a.m. until they meet. Total time = 1 hour (from 8:00 to 9:00) + 48 minutes = 1 hour 48 minutes They meet 1 hour 48 minutes after 8:00 a.m. 1 hour 48 minutes b) At what time do they meet? Step 1: Determine the meeting time. They start moving towards each other at 9:00 a.m. and meet 48 minutes later. Meeting time = 9:00 a.m. + 48 minutes = 9:48 a.m. 9:48 a.m. Send me the next one 📸