Question

Two trains are travelling between two stations at a constant speed of 25kmph.The stations are 50km apart .A bird travelling at 100kmph starts its flight along with one train and travels in the same direction until it meets the other train. It changes its direction and goes in the reverse direction until it meets the initial train. Find the distance travelled by the bird before the two trains collide.

Answer 1

Answer:

100 km

Explanation:

Both the trains will meet each other exactly after 1hr since both have the same speeds. So distance covered by the bird is 100km/hr * 1hr = 100km

Answer 2

The answer is 100 km.

Given:

The speed of both trains is 25 kmph

The stations are 50 km apart

The bird travels at 100 kmph.

To Find:

The distance travelled by the bird before the two trains collide

Solution:

Initially, the relative speed of the bird w.r.t the second train = 100+25=125

The distance between the bird and the second train = 50

Hence the time taken for the bird to reach the second train is

$=\frac{50}{125}=\frac{2}{5}$

Therefore the distance travelled by the bird in this time

$d_1=100*\frac{2}{5}=40 km$

In this time, the distance travelled by the first train is

$25*\frac{2}{5} =10 km$

Hence the distance between the bird and the first train is 30 km.

The relative speed of the bird w.r.t the first train = 100+25=125

Hence the time taken to reach the first train is

$=\frac{30}{125} = \frac{6}{25}$

The distance travelled by the bird in this time is

$d_2=100*\frac{6}{25}= 24 km$

The distance travelled by the first and second trains in this time is

$25*\frac{6}{25}=6$

Hence the distance between the bird and the second train is 24-6=18 km

The time taken by the bird to reach the second train again is

$\frac{18}{125}$

Hence the distance travelled by the bird is

$d_3=100*\frac{18}{125}=14.4 km$

Hence we can see the distances are in a GP with a common ratio of 0.6.

Hence the total distance travelled by the bird will be according to the infinite GP formula $\frac{a}{1-r}$ where a is the initial term and r is the common ratio.

$d=\frac{40}{1-0.6}=100 km$

The distance travelled by the bird before the two trains collide is 100 km.

#SPJ2