To find the distance of the meeting point from Town A, we can break down the problem step by step.
Step 1: Understand the Problem
- Distance between Town A and Town B: 1150 km
- Speed of the bus: 60 km/h (leaves Town A at 07:00)
- Speed of the car: 80 km/h (leaves Town B at 07:30)
Step 2: Determine the Time Until They Meet
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Time Delay: The bus starts first, which means it will travel alone for 30 minutes (or 0.5 hours) before the car starts.
- In 0.5 hours, the bus travels: \[ \text{Distance by bus} = \text{Speed} \times \text{Time} = 60 , \text{km/h} \times 0.5 , \text{h} = 30 , \text{km} \]
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Remaining Distance: After the bus has traveled 30 km, the distance left between the bus and car to meet is: \[ \text{Remaining distance} = 1150 , \text{km} - 30 , \text{km} = 1120 , \text{km} \]
Step 3: Calculate the Time to Meet
From this point, both the bus and the car are approaching each other. We can combine their speeds to find out how long it will take them to meet.
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Combined Speed: \[ \text{Combined speed} = \text{Speed of bus} + \text{Speed of car} = 60 , \text{km/h} + 80 , \text{km/h} = 140 , \text{km/h} \]
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Time to meet: To find out how long it will take to cover the remaining distance: \[ \text{Time} = \frac{\text{Remaining distance}}{\text{Combined speed}} = \frac{1120 , \text{km}}{140 , \text{km/h}} = 8 , \text{hours} \]
Step 4: Calculate the Distance from Town A
Now that we know the time to meet after the bus has started traveling alone for 0.5 hours, we can find out how far each vehicle travels until they meet.
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Distance traveled by the bus during the 8 hours: \[ \text{Distance by bus} = \text{Time} \times \text{Speed} = 8 , \text{h} \times 60 , \text{km/h} = 480 , \text{km} \]
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Total distance traveled by the bus from Town A:
- Add the distance the bus traveled alone before the car started (30 km): \[ \text{Total distance by bus} = 30 , \text{km} + 480 , \text{km} = 510 , \text{km} \]
Step 5: Conclusion
The distance of their meeting point from Town A is 510 km.