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   Fog Creek Home