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.
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You're on a roll — Here's the solution to the problem: i) The time the Lamu Bus arrived in Nairobi. Step 1: Calculate the time taken by the Lamu bus to travel from Mombasa to Nairobi. The distance between Nairobi and Mombasa is 400 km. The speed of the Lamu bus is 120 km/hr. Time = DistanceSpeed Time taken by Lamu bus = 400 km120 km/hr = (10)/(3) hours Convert the time to hours and minutes: (10)/(3) hours = 3 (1)/(3) hours = 3 hours + ((1)/(3) × 60) minutes = 3 hours 20 minutes Step 2: Calculate the arrival time of the Lamu bus in Nairobi. The Lamu bus left Mombasa at 8:30 a.m. Arrival time = 8:30 a.m. + 3 hours 20 minutes = 11:50 a.m. The Lamu Bus arrived in Nairobi at 11:50 a.m.. ii) The time the two buses met. Step 1: Calculate the distance covered by the Coast bus before the Lamu bus started. The Coast bus left Nairobi at 8:00 a.m. The Lamu bus left Mombasa at 8:30 a.m. Time difference = 30 minutes = 0.5 hours. Speed of Coast bus = 80 km/hr. Distance covered by Coast bus in 0.5 hours = 80 km/hr × 0.5 hr = 40 km Step 2: Calculate the remaining distance between the buses at 8:30 a.m. Total distance = 400 km. Remaining distance = 400 km - 40 km = 360 km Step 3: Calculate the relative speed of the two buses. The buses are moving towards each other. Speed of Coast bus = 80 km/hr. Speed of Lamu bus = 120 km/hr. Relative speed = 80 km/hr + 120 km/hr = 200 km/hr Step 4: Calculate the time taken for the buses to meet from 8:30 a.m. Time to meet = Remaining distanceRelative speed = 360 km200 km/hr = (18)/(10) hours = 1.8 hours Convert 1.8 hours to hours and minutes: 1.8 hours = 1 hour + (0.8 × 60) minutes = 1 hour 48 minutes Step 5: Determine the meeting time. The buses started moving towards each other at 8:30 a.m. Meeting time = 8:30 a.m. + 1 hour 48 minutes = 10:18 a.m. The two buses met at 10:18 a.m.. iii) The distance from Nairobi to the point where the buses met. Step 1: Calculate the total time the Coast bus traveled until it met the Lamu bus. The Coast bus left Nairobi at 8:00 a.m. and met at 10:18 a.m. Total travel time for Coast bus = 10:18 a.m. - 8:00 a.m. = 2 hours 18 minutes Convert 18 minutes to hours: 18 minutes = (18)/(60) hours = 0.3 hours. Total travel time for Coast bus = 2 + 0.3 = 2.3 hours Step 2: Calculate the distance covered by the Coast bus from Nairobi. Speed of Coast bus = 80 km/hr. Distance from Nairobi = Speed × Time = 80 km/hr × 2.3 hours = 184 km The distance from Nairobi to the point where the buses met is 184 km. iv) How far Coast Bus is from Mombasa when Lamu bus arrives in Nairobi. Step 1: Determine the arrival time of the Lamu bus in Nairobi. From part (i), the Lamu bus arrived in Nairobi at 11:50 a.m. Step 2: Calculate the total time the Coast bus traveled until 11:50 a.m. The Coast bus left Nairobi at 8:00 a.m. Total travel time for Coast bus = 11:50 a.m. - 8:00 a.m. = 3 hours 50 minutes Convert 50 minutes to hours: 50 minutes = (50)/(60) hours = (5)/(6) hours. Total travel time for Coast bus = 3 + (5)/(6) = (18)/(6) + (5)/(6) = (23)/(6) hours Step 3: Calculate the distance covered by the Coast bus from Nairobi. Speed of Coast bus = 80 km/hr. Distance covered by Coast bus = 80 km/hr × (23)/(6)