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How far will the bird have flown?
A train leaves Town A and travels toward Town B at a constant speed of 60 km/h. At the same time, another train leaves Town B and travels toward Town A at a constant speed of 90 km/h. The distance between Town A and Town B is 450 km. If a bird starts flying from Town A at the same time as the first train leaves, and it flies back and forth between the two trains at a constant speed of 120 km/h until the trains meet, how far will the bird have flown?
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2 Replies
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To solve this problem, we need to understand the relative motion of the trains and the bird. Let’s break it down step by step:
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The first train is traveling from Town A to Town B at a constant speed of 60 km/h. We can calculate the time it takes for this train to reach Town B using the formula: Time = Distance / Speed Time = 450 km / 60 km/h = 7.5 hours
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At the same time, the second train is traveling from Town B to Town A at a constant speed of 90 km/h. Since the two trains are moving towards each other, we can consider their combined speed: Combined Speed = Speed of Train A + Speed of Train B Combined Speed = 60 km/h + 90 km/h = 150 km/h
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Now, we can calculate the time it takes for the two trains to meet by dividing the distance between Town A and Town B by their combined speed: Time = Distance / Combined Speed Time = 450 km / 150 km/h = 3 hours
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The bird starts flying from Town A at the same time as the first train leaves and continues flying until the trains meet. Since the bird flies back and forth between the two trains, we need to calculate the total distance it covers. We can calculate this by multiplying the bird’s speed by the time it takes for the trains to meet: Distance = Speed × Time Distance = 120 km/h × 3 hours = 360 km
Therefore, the bird will have flown a total distance of 360 kilometers.
In summary, the bird will fly 360 kilometers while shuttling between the two trains until they meet.
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To solve this problem, we need to determine the time it takes for the two trains to meet. Once we know the meeting time, we can calculate the distance the bird has flown.
Let’s start by finding the meeting time of the trains. Since they are moving towards each other, we can use the concept of relative speed.
The relative speed of the two trains is the sum of their individual speeds: Relative speed = Speed of train A + Speed of train B
Relative speed = 60 km/h + 90 km/h Relative speed = 150 km/h
Now, we can use the formula: Time = Distance / Speed
Time = 450 km / 150 km/h Time = 3 hours
Therefore, it will take 3 hours for the two trains to meet.
Now, let’s calculate the distance the bird will have flown during this time.
Since the bird is flying back and forth between the two trains, we can consider the bird’s speed relative to the trains. The relative speed of the bird with respect to the trains is the difference between their speeds: Relative speed = Speed of bird – Speed of train A (or train B)
Relative speed = 120 km/h – 60 km/h (since the bird is flying towards the train)
Relative speed = 60 km/h
Now, we can use the formula: Distance = Speed x Time
Distance = 60 km/h x 3 hours Distance = 180 km
Therefore, the bird will have flown a distance of 180 kilometers when the trains meet.
Note: The bird’s speed and direction are such that it can easily maintain the same distance from each train as they move towards each other.
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