The railroad bridge across the Futile Mire has a northbound track and a southbound track. The tracks are parallel and exactly 2 miles long. Anyone attempting to cross the bridge on foot must stay between the rails on the chosen track. It is not possible to step outside the rails or to jump to the other track.
One day Tom and Sue try to walk across the bridge, Tom heading north on the northbound track, and Sue heading south on the southbound track. The athletic Sue can run twice as fast as the portly Tom. All trains run at the same constant speed.
When Tom and Sue are 1 mile apart they both hear trains whistles behind them. Trains are approaching on both tracks. Tom and Sue can just escape by running to either end of the bridge. How far is each train from the tunnel?

• 
  T_________A____P_________B
  
  ...................C________ ___Q__D_____t
  
  AB and CD are the two tracks. P is the position of Sue and Q is the position of Tom when they heard the noise of trains.
  
  AP = 2/3 miles and DQ = 1/3 miles
  
  T and t are position of trains.
  
  Let AT = x miles and Dt = y miles
  
  Then,
  x/(2/3) = (x + 2)/(4/3) {as ratio of distances travelled of Sue and train will be equal in both cases}
  x = 2 miles
  
  Similarly, y/(1/3) = (y + 2)/(5/3)
  y = 0.5 miles
  
  Hence, distance between the trains = 2+2+0.5 = 4.5 miles
• 15 years agoHelpfull: Yes(1) No(1)