Question

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?

Answer 1

Answer:

The total distance the bird travels is d.

Explanation:

Each train travels at the speed s. They will meet at the center, a distance d/2 (which is where the bird might be crushed). Each train travels the same distance d/2 in a time t which is also equal for both. This is also the time the bird spends travelling between them.

For any of the train, the time t is the distance divided by the speed.

$t = \dfrac{d/2}{s} = \dfrac{d}{2s}$

The bird travels at the speed of 2s. Its distance is given by the product of its speed and the time taken.

$d_\text{Bird} = \dfrac{d}{2s}\times 2s = d$