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 problem: a) At which time did Kagwa and Manzi meet? Step 1: Calculate the distance Kagwa covered before Manzi started. Kagwa started at 7:00 am and Manzi started at 9:00 am. Time difference = 9:00 am - 7:00 am = 2 hours. Distance covered by Kagwa in 2 hours: Distance = Speed × Time Distance_Kagwa initial = 80 km/hr × 2 hr = 160 km Step 2: Calculate the remaining distance between them when Manzi started. Total distance between Town A and Town B is 520 km. Remaining distance = Total distance - Distance Kagwa initial Remaining distance = 520 km - 160 km = 360 km Step 3: Calculate their relative speed. Since they are moving towards each other, their speeds add up. Relative speed = Speed_Kagwa + Speed_Manzi Relative speed = 80 km/hr + 100 km/hr = 180 km/hr Step 4: Calculate the time it took for them to meet after Manzi started. Time to meet = Remaining distanceRelative speed Time to meet = 360 km180 km/hr = 2 hours Step 5: Determine the meeting time. They met 2 hours after Manzi started (9:00 am). Meeting time = 9:00 am + 2 hours = 11:00 am The time Kagwa and Manzi met is 11:00 am. b) Find the distance covered by Kagwa. Step 1: Calculate the total time Kagwa traveled until they met. Kagwa traveled for 2 hours before Manzi started, and then another 2 hours until they met. Total time Kagwa traveled = 2 hours + 2 hours = 4 hours Step 2: Calculate the distance covered by Kagwa. Distance_Kagwa = Speed_Kagwa × Total time Kagwa traveled Distance_Kagwa = 80 km/hr × 4 hours = 320 km The distance covered by Kagwa is 320 km. c) Find the distance covered by Manzi. Step 1: Calculate the total time Manzi traveled until they met. Manzi started at 9:00 am and they met at 11:00 am. Total time Manzi traveled = 11:00 am - 9:00 am = 2 hours Step 2: Calculate the distance covered by Manzi. Distance_Manzi = Speed_Manzi × Total time Manzi traveled Distance_Manzi = 100 km/hr × 2 hours = 200 km The distance covered by Manzi is 200 km. 3 done, 2 left today. You're making progress.