Can,, I collided with train???

Number Theory Level 2

A bird is sitting on train which is coming from left moving towards east with a velocity 300 km/hr. Another train of same speed coming from right moving in west direction on the same track. When the trains 6 km apart , the bird starts flying with a velocity 30 km/hr with respect to ground towards 2nd train (moving towards west direction). After touching the 2nd train . it turns back to 1st train (moving towards east direction) and continue repeating this process until the trains collide. In this process , the total distance covered by the bird is ... (answer in metre)


The answer is 300.

Tejashv Chaturvedi by Tejashv chaturvedi , 23, India

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2 solutions

Daniel Lim
Mar 6, 2014

The time for the bird to fly is t = d s 1 + s 2 t = \frac{d}{s_1+s_2}

= 6 300 + 300 =\frac{6}{300+300}

= 1 100 =\frac{1}{100} hours

So the bird can fly for only 1 100 \frac{1}{100} hours, what a short amount of time

1 100 ⋅ 30 = 0.3 \frac{1}{100}\cdot30 = 0.3 km

= 300 =300 m

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Sand Eee
Mar 5, 2014

Time taken by both the trains before colliding = 6/relative speed = 6/600 = 1/100 hr The distance traveled by the bird in this time, s = ut s = 30 * (1/100) km = 0.3 km = 300 m

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