A train travels at a particular speed for a duration of one hour, after which one of its engine malfunctions reducing its speed to 3/5th of the actual speed before the occurrence of fault in engine. It travels at this speed for 2 hours to reach at its destination. If the fault had occurred 50 miles later on, the train would have reached its destination 45 minutes early. Find the distance traveled by the train.

• Let the actual speed of train be X miles/hour.
  Let the initial distance covered by train is d1.
  After fault its speed will be reduced to 3X/5 miles/hour.
  So the distance travelled is (3X/5) * 2 = 6X/5 = d2 ----> (i)
  So total distance = X + 6X/5 = 11X/5
  Now if the fault had occurred at d1 + 50
  3X/5 * 5/4 = d2 - 50 -----> (ii)
  subtracting (ii) from (i)
  (i) - (ii) = (6X/5) - (3X/4) = 50
  9X/20 = 50 or X = 1000/9
  So the distance d2 = 133.33 miles
  So d1 = 11*1000/(9*5) - 133.33 = 111.11
  So total distance is 133.33+111.11 = 244.44 miles
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