From two towns 600 km apart, two buses, A and B, start simultaneously at 6 am towards each other. They move with constant speeds till each reaches its destination town. It takes 5 hours for A to reach its destination and 7.5 hours for B to reach its destination. At what time do the two buses meet?
Question
From two towns 600 km apart, two buses, A and B, start simultaneously at 6 am towards each other. They move with constant speeds till each reaches its destination town. It takes 5 hours for A to reach its destination and 7.5 hours for B to reach its destination. At what time do the two buses meet?
Solution
To solve this problem, we first need to find the speeds of both buses.
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Speed of Bus A: The speed of a vehicle is given by the formula Speed = Distance/Time. Here, the distance is 600 km and the time taken by Bus A is 5 hours. So, the speed of Bus A = 600 km / 5 hours = 120 km/hour.
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Speed of Bus B: Similarly, the speed of Bus B = 600 km / 7.5 hours = 80 km/hour.
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Now, we need to find the time when the two buses meet. When two objects move towards each other, their relative speed is the sum of their individual speeds. So, the relative speed of the two buses = 120 km/hour + 80 km/hour = 200 km/hour.
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The time when two objects meet is given by the formula Time = Distance / Relative Speed. Here, the distance is 600 km and the relative speed is 200 km/hour. So, the time when the two buses meet = 600 km / 200 km/hour = 3 hours.
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The two buses started at 6 am. So, they meet at 6 am + 3 hours = 9 am.
Therefore, the two buses meet at 9 am.
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