**Maths Logical Problem - 7 November**

Accidentally, two trains are running in the opposite direction and enter a tunnel that is 200 miles long. A supersonic bird that has fled the lab and taken shelter in the tunnel starts flying from one train towards the other at a speed of 1000 mph. As soon as it reaches the second train, he starts flying back to avoid collision and meets the first train again at the other end. The bird keeps flying to and fro till the trains collide with each other.

What is the total distance that the supersonic bird has traveled till the trains collided ?

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100 miles

ReplyDeleteLet the speed of each train be 'v mph' so that their relative speed is 2v (assuming both travels with same speed)

ReplyDeleteTherefore time taken for collision will be:

200/2v (Relative Distance/ Relative Speed)=100/v.

Now in this time the supersonic bird will move a distance of (100/v)*1000=100000/v.(Distance=time*speed)

Where v is the speed of each train.

Therefore we must be given the speed of the train to calculate the final answer.

If the trains are travelling slow, the bird will make many more trips back and forth than if the trains are travelling fast. The answer must be expressed as a computation of the combined speed of the trains to arrive at time to collision in the 200 mile tunnel, then bird distance is 1000mph for that computed collision time. Need train speed(s), else a formula is the best we can do.

ReplyDeleteI think you guys are thinking to much, I may be wrong, but the answer I think is 200mlies. The bird only travelled a distance of 200miles, cus going to and fro has already been travelled!!

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ReplyDeletelet speed of train=d

ReplyDeletetotal distance from train to end= 200*2=400

total distance the bird has to fly=400+{400-d}+{400-2d}+....+0

=n/2{800-(n-1)d}

The bird flies at a constant speed. So we just have to figure out the flying time, which is the time it takes the trains to collide.

ReplyDelete(200 /(d*2)) * 1000 = distance traveled.

This only works of the trains are heading towards each other, and if the birds acceleration is instantaneous.

ReplyDeleteTrains are travelling in opposite directions. They will never meet and bird is still flying ;)

ReplyDeleteTrains are travelling in opposite directions. They will never meet and bird is still flying ;)

ReplyDelete