Two trains, each having a speed of s, are headed at each other on the same straight track. A bird that can fly at speed 2s flies off the front of one train when they are d apart and heads directly for the other train. On reaching the other train it flies directly back to the first train, and so forth. (We have no idea why a bird would behave in this way.) In terms of variables given in the problem, what is the total distance the bird travels?
The answer is d.
2s(d/s1+s2) = 2s(d/2s) = d
To find the total distance the bird travels, we need to consider the distances it travels in each trip.
Let's assume that the time taken for the bird to fly from one train to the other is t.
In time t, the first train would have traveled a distance of s*t, and the second train would have traveled a distance of s*t as well.
So, the total distance between the two trains covered in time t is (s*t + s*t) = 2s*t.
Now, let's consider the distance traveled by the bird itself. The bird flies at a speed of 2s, and the time taken to travel the distance d is d/(2s) = t.
Since the bird travels the same distance back and forth when it reaches each train, the total distance covered by the bird in time t is 2 * d.
Now, given that the total distance covered by the bird in time t is 2 * d, and the total distance between the trains covered in time t is 2s*t, we can equate the two distances:
2 * d = 2s * t
Simplifying the equation, we get:
d = s * t
Therefore, the total distance the bird travels is equal to d.