Here's the question:
Consider two stations A and B located 100 kilometer apart. There is a station C, located between A and B. Now trains from station A and B start moving towards station C at different speeds. The train starting from A moves at 40 km/h while the train starting from B moves at 60 km/h. These trains have to stop at station C. A bird also starts from station B and flies at a speed of 80 km/h towards station A. When it reaches the train coming from station A, it switches direction – flying back towards station B and when it reaches the train coming from station B, it turns around again, heading towards the direction of station A. This goes on for some time till both the trains reach station C. What is the total distance covered by the bird in the time it takes for the two trains to reach station C?
This is what I thought:
The distance travelled by the bird should depend on location of station C.
Reason: If Ta and Tb is the time taken by the trains to reach station C respectively, and the bird will have to keep on flying until both trains reach station C, the time for which the bird will have to fly is max(Ta, Tb).
So the answer should be max(Ta, Tb) x 80.
The fact that the answer will depend on location of C can also be verified by taking 2 cases. In the first case, let C be 1km from station A, and in the other one, let C be 1km from station B. You will get different answers.
However, apparently my answer is wrong, as the answer was asked in an exam and had a unique answer (independent of any variable).
Can someone please explain where I went wrong?