Two trains, each having a speed of 30 km/h, are headed attach other on the same straight track. A bird that can fly 60 km/h flies off the front of one train when they are 60 km apart and heads directly for the other train. On reaching the other train, the bird flies directly back to the first train, and so forth. What is the total distance the bird travels before the trains collide?
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Since, the speed of bird is 60 km/h’.
In this problem the bird flies at a constant speed for the entire time and the trains travel until colliding. The distance the bird travels is thus
d = vt
We need to compute the time that the trains run before colliding. By symmetry, we can argue that the trains will collide in the middle, at 30 km. The time to collision is simply the time for either train to travel 30 km, which is 1 hour. Now that we know how long the trains will run, we can see that the distance the bird will travel is (60 km/h)(1 h) = 60 km.
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