A train blows a siren one hour after starting from the station. After that it travels at 3/5th of its speed it reaches the next station 2 hours behind schedule. If it had a problem 50 miles farther from the previous case,it would have reached 40 minutes sooner. Find the distance between the two stations

• Total distance = 200 miles
  original speed = 50 mph
  
  sol
  
  If S is speed and t is original time as per schedule, then
  Distance = S*t
  
  
  In first case,
  Distance left after 1 hr journey = S(t-1) = (3/5)*S*(t+2-1)
  
  solving it, we get , t= 4 hrs. hence total distance = 4S miles.
  
  In second case,
  If it had a problem 50 miles farther from the previous case,it would have reached 40 minutes sooner.
  
  (4S-S-50)/(S*3/5) +(S+50)/S = 4+2-2/3 = 16/3
  
  solving it, we get , speed S = 50 mph
  
  Check..
  In 1st case it travelled 1 hr @ 50 mph and for next 5 hrs @ 30 mph.
  In 2nd case, it travelled 100 miles @ 50 mph in 2 hrs and next 100 miles @ 30 mph in 3 1/3 hrs.
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