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Two trains , each having a speed of 30km/h, are headed at each other on the same straight track . A bird that can fly 60 km/h flies off the front of one train when they are 60 km apart and heads directly for other train . On reaching the other train , the bird flies directly back to the first train and so forth . What is the total distance the bird travels before the trains collide ?

7 years ago

relative velocity of train wrt the other train is 30-(-30)=60km/h

relative distance is 60 km

therefore time taken for collision is 60km/60km/h= 1hr

total distance the bird will cover in 1hr = 60km/h * 1h=60km

4 years ago

Each train is having a speed of 30km/hr.

Their initial relative distance is 60km.

The bird flies off the front of the first train when both the trains are 60km apart from each other.

Speed of the bird=60km/hr

Relative distance=Relative speed*Time

Relative speed is the sum of the speeds of two objects when they are moving towards each other or in opposite directions and it is the difference of the speeds of the objects when they are moving in the same direction.

Here,

time taken for the bird to meet the second train coming in opposite direction=60km/(30+60)km/hr=60/90hrs=2/3hours

distance travelled by the bird when it meets the second train=2/3hrs*60km/hr=40km

distance travelled by the second train=2/3hrs*30km/hr=20km

So,after the bird reaches the second train ,the bird has travelled 40km and the train 20km.

Distance travelled by the first train in 2/3hrs=2/3hrs*30km/hr=20km

Now the bird sets off from the second train with a speed of 60km/hr and from a distance of 20km from the first train as their relative separation now has become

20km{40km(distance travelled by the bird on reaching the train B)-20km(distance travelled by train A)}

Time taken for the bird to reach back train A=Relative distance(20km)/Relative speed(60km/hr+30km/hr)

=20/90hrs=2/9hrs

Distance travelled by the bird in the direction of train B=2/9hrs*60km/hr=40/3km

5 months ago

The answer will be 60km and it'll take the bird infinite number of trips to do that.

In its first flight

The bird will meet the train in time t1=2/3hr and travel a distance S1=40km. During this time period the trains would also cover a distance of 20km each, now the remaining distance between both of them is 20km.

In second flight

The bird will meet the train in time t2=2/9hr and will travel a distance S2=40/3km. During this time period the trains would also cover a distance of 20/3km each and now the remaining distance between them would be 20/3km.

Similarly we will get a patter of infinite trips

t3=2/27hr and S3=40/9km

t4=2/81hr and S4=40/27km

......

This is an infinite GP

Total distance will be

= (40 + 40/3 + 40/9 + 40/27........)km

= 60km

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