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Question

A journey 192 km from town A to town B take 2 hrs more by an ordinary passenger train than a dupe train . If the speed of the frighten train is 16 km/hr more. Find the speed of the fate is the passenger train .

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Solution

  • Let the speed of the average passenger train be 'x' km/hr.
  • So, the time taken by the passenger train = 192/x.
  • So, the average speed of the super fast train = (x + 16) km/hr
  • So, the time taken by the super fast train = 192/(x + 16).
  • Given : Time taken by the passenger train to travel 192 km - time taken by super fast train to cover the distance of 192 km = 2 hours.
  • Therefore,
  • 192/x - 192/(x + 16) = 2 Taking L.C.M.. we get
  • (192x + 3072 + 192x)/(x)(x+16) = 2
  • 3072/x(x + 16) = 2 After cross multiplying, we get
  • 3072 = 2x² + 32x
  • 2x² + 32x - 3072 = 0
  • Dividing it by 2, we get
  • x² + 16x - 1536 = 0
  • x² + 48x - 32x - 1536 = 0
  • x(x + 48) - 32(x + 48) = 0
  • (x + 48) (x - 32) = 0
  • x = - 48 or x = 32
  • The speed of the train cannot be negative, therefore the speed of the passenger train is 32 km/hr
And the speed of the super fast train is 32 + 16 = 48 km/hr



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