railroad bridge
The answer is :
The train's speed is 8 times faster than the Man's speed.
Assuming the bridge lenght is X and the distance of the train from the bridge is Y, we can compose the following equations :
1/4X Y
 = 
Ms Ts
3/4X Y+X
 = 
Ms Ts
Where "Ms" is the Man's Speed and "Ts" is the Train's Speed.
You get : Ts = 8*Ms
Rami Tomer
Monday, August 4, 2003
Corection : The train goes 2 times faster than the man.
Rami Tomer
Monday, August 4, 2003
There's an "aha" way to solve this:
In the time it takes for the man to run 1/4 of the bridge distance, the train reaches the bridge. If he tries to run the long way, then the train reaches the bridge when the man is halfway across the bridge (since he starts at the 1/4 point).
Now it's just a problem of a man is halfway across a bridge, and a train is just entering the bridge, and we know that they both reach the other end at the same time, so the train has to be going twice as fast as the man.
Tim H
Wednesday, August 6, 2003
The Aha way is definitely a different way of solving the problem. To be more explanative on the mathematical solution:
TimetrainBT = time taken by train to reach the beginning fo the tunnel
TimetrainET = time taken by train to reach the end of the tunnel
similarly
TimemanBT = time taken by man to ....
TimemanET = time taken by man to ....
since TimetrainBT = TimemanBT 1
TimetrainET = TimetrainET 2
therefore
Trainspeed Manspeed
1 corresponds to  = 
DistancetrainBT DistmanBT
similar equation for 2
Assuming the train's distance from the tunnel is D
and the tunnel is X units long we have
Trainspeed Manspeed
 =  for 1
D 1/4 X
and
Trainspeed Manspeed
 =  for 2
D + X 3/4X
using 1 we get the value of
Trainspeed * X
D =  as 3
4 * Manspeed
Replace 3 in 2 to get Trainspeed = 2*Manspeed
Hadi Mohammed
Thursday, August 7, 2003
Can I rephrase the "aha" way in case it makes it clearer (for those who think like I do)?
There are two ways for the man to go, backwards or forwards. One way is three quarters of a tunnel, the other is one quarter of a tunnel, so the difference between the two narrow escapes is half a tunnel.
From the train's point of view the difference between the two narrow escapes is a whole tunnel.
Therefore the train goes a whole tunnel in the time it takes the person to go half a tunnel.
lionel
Wednesday, August 13, 2003
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