Bird's Journey From Train To Train

Suppose distance between SECUNDERABAD & CST is 1000 KM. Railway tracks are in straight lines with no curves in between.

A train with uniform speed of 100 kmph departs from CST at 9:00 AM. Same day on same track other train from SECUNDERABAD departs at 10:00 AM with uniform speed of 80 kmph.

A bird sitting on engine of train that departed from CST starts traveling toward the SECUNDERABAD & after touching the engine of that train travels back to CST train. A bird repeats this until trains collide.

How much distance the bird traveled & how many times did it travel to & fro? 

Click for the answer! 

Distance Traveled By The Bird

Here is the question! 

Let's divide answer in 2 parts.

1.Finding distance traveled by the bird.

The SECUNDERABAD train is one hour late till then CST train covers 100 km.

Hence effective distance is 900 km

Total speed of approach = 100 + 80 kmph

Total distance covered = 900 km

Time passed before trains collide = 900/180 = 5 Hours

Speed of bird = 120 kmph

Distance covered in 5 hours by bird = 120 * 5 = 600 km

Distance covered in first hour by bird = 120 km

Total distance = 600 + 120 = 720 km



2. Finding how many times bird traveled back & forth.


1st travel -

Total speed of approach = 120 + 80 = 200 kmph

Total distance to be covered = 900 km

Time required to meet each other = 900/200 = 4.5 Hours.
 
2nd travel -

Distance traveled by CST train in 4.5 hours = 100 x 4.5 = 450km

Distance traveled by SECUNDERABAD train in 4.5 hours = 80 x 4.5 = 360 km

Distance between 2 trains = 900 - (450+360) = 90 km

Time left for collision is 5 - 4.5 = 0.5 hrs.


So bird ends up with 1 complete round.