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
To calculate the time the car arrived in Nairobi, we must first determine the total distance travelled and the time taken for the journey. The question implies a round trip since the car left Nairobi and "arrived in Nairobi" after covering a distance related to Busia. Assumptions: The car travels from Nairobi to Busia and then returns to Nairobi. The average speed of 120 km/h applies to the entire round trip. Step 1: Calculate the total distance travelled by the car. The distance between Nairobi and Busia is 400 km. For the car to leave Nairobi and arrive back in Nairobi, it must complete a round trip. Total Distance = Distance (Nairobi to Busia) + Distance (Busia to Nairobi) Total Distance = 400 km + 400 km Total Distance = 800 km Step 2: Calculate the time taken for the car to complete the journey. The formula for time is: Time = DistanceSpeed Given the car's average speed is 120 km/h. Time = 800 km120 km/h Time = (80)/(12) hours Simplify the fraction: Time = (20)/(3) hours Step 3: Convert the total travel time into hours and minutes. (20)/(3) hours = 6 (2)/(3) hours To convert the fractional part to minutes: (2)/(3) hours × 60 minutes/hour = 40 minutes So, the total travel time is 6 hours and 40 minutes. Step 4: Calculate the car's arrival time in Nairobi. The car left Nairobi at 8:30 am. Arrival Time = Departure Time + Travel Time Arrival Time = 8:30 am + 6 hours 40 minutes Adding the hours: 8 + 6 = 14 hours. Adding the minutes: 30 + 40 = 70 minutes. Since 70 minutes is 1 hour and 10 minutes, we add this to the hours: 14 hours + 1 hour 10 minutes = 15 hours 10 minutes Converting to 12-hour format (pm): 15:10 is 3:10 pm. The time the car arrived in Nairobi is 3:10 pm.