Railroad Bridge
a man needs to go through a train tunnel. he starts through the tunnel and when he gets 1/4 the way through the tunnel, he hears the train whistle behind him. you don't know how far away the train is, or how fast it is going, (or how fast he is going). all you know is that
1. if the man turns around and runs back the way he came, he will just barely make it out of the tunnel alive before the train hits him.
2. if the man keeps running through the tunnel, he will also just barely make it out of the tunnel alive before the train hits him.
assume the man runs the same speed whether he goes back to the start or continues on through the tunnel. also assume that he accelerates to his top speed instantaneously. assume the train misses him by an infintisimal amount and all those other reasonable assumptions that go along with puzzles like this so that some wanker doesn't say the problem isn't well defined.
how fast is the train going compared to the man?
Answer
Trains is moving 4 times the speed of man.
!-----------------------!----------!--------------------!
A B C D
AC is tunnel. Man is at B and AB = 3 * BC. Trains is at D when man hears the sound. Let CD = y.
Assume that SM and ST are mans and trains speed respt.
So as per conditions x/SM = y/ST so ST = (y/x)*SM
Now x/ST+SM = 3x/ST-SM
Substitute ST in terms of SM from 1st equation and solve to get relation between x and y. The relations comes as y = 4x.
Hence the ST = (4x/x)*SM = 4 * Mans Speed.
Let the distance of the
Let the distance of the tunnel be "a"
Let the distance between the train and the entrance of the tunnel be "b"
Let the speed of the man be "m"
Let the speed of the train be "t"
let's calculate the speed of the train compared to that of the man if they were to meet exactly at the entrance or the exit of the tunnel
t/b = m/(1/4 x a)
t/b = 4m/a
t/b + t/a = m/(3/4 x a)
t/b + t/a = 4m/3a
t/b = 4m/3a - t/a = 4m/a
4m/3 - t = 4m
16m/3 = t
hence for the man to collide with the train at both the entrance and exit, the train has to be 16/3 times faster than the man
therefore for the man to survive, the train is traveling just lesser than 16/3 faster