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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.