To find out how far from Busia the bus and the car meet, we can calculate the distance each vehicle travels until they meet.
Step 1: Time Calculation
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Bus Departure:
- The bus leaves Busia at 7:30 AM at a speed of 90 km/h.
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Car Departure:
- The car leaves Nairobi at 9:30 AM at a speed of 120 km/h.
Step 2: Distance and Time Before Meeting
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Travel Time of the Bus Before Car Starts:
- The bus travels for 2 hours before the car departs (from 7:30 AM to 9:30 AM).
- Distance traveled by the bus in 2 hours: \[ \text{Distance (Bus)} = \text{Speed} \times \text{Time} = 90 , \text{km/h} \times 2 , \text{hours} = 180 , \text{km} \]
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Remaining Distance:
- The total distance between Busia and Nairobi is 360 km.
- After 2 hours, the distance between the bus (which is 180 km from Busia) and the car (which is at Nairobi) is: \[ \text{Remaining Distance} = 360 , \text{km} - 180 , \text{km} = 180 , \text{km} \]
Step 3: Combined Speed
- After 9:30 AM, both the bus and the car are moving towards each other.
- Combined speed of the bus and the car: \[ \text{Combined Speed} = 90 , \text{km/h} + 120 , \text{km/h} = 210 , \text{km/h} \]
Step 4: Time to Meet
- Time taken to cover the remaining distance of 180 km: \[ \text{Time to meet} = \frac{\text{Remaining Distance}}{\text{Combined Speed}} = \frac{180 , \text{km}}{210 , \text{km/h}} \approx 0.857 , \text{hours} \approx 51.4 , \text{minutes} \]
Step 5: Meeting Point
To find the distance from Busia to the meeting point:
- Distance traveled by the bus in 51.4 minutes (which is approximately 0.857 hours): \[ \text{Distance (Bus to meeting point)} = 90 , \text{km/h} \times 0.857 , \text{hours} \approx 77.14 , \text{km} \]
Final Answer
The bus and the car meet approximately 77.14 km from Busia.