we can set up the equations
(5/8)(120)/S = (120+X)/T
(3/8)(120)/S = X/T
where X is the distance from the train to the bridge
T is the speed of the train
and S is your speed.
Solving gives T=4S, meaning the train is 4 times as fast as you. So, the distance from you is 4x your distance from the other side, 4*120*5/8= 300 m ?
I have changed the question being asked in this scenario that AmazingAryan posted a while back:
Walking home one day, you take a short cut along the train tracks. The tracks cross a narrow bridge over a deep gorge. At the point you are 3/8 of the way across the bridge, you hear the train whistle somewhere behind you. You charge across the bridge, and jump off the track as the train is about to run you down. As it happens, if you had gone the other way, you would have reached safety just before being run over as well.
If the bridge is 120 meters long, how far from you was the train when you heard the whistle?