<PRE><B>Question 1199</B>
 Let V km/hr be the speed of the bullet train and so the speed of the 
 existing train is V - 40.

 The time for the the bullet train to finish the whole journey is
  850/V, while it takes 850/(V-40) hr for the existing train for the
  journey. Since we know the time difference is 3 hrs, we have

 3 + 850/V = 850/(V-40),

 Cancel the denominator by multiply V(V-40):
 3V(V-40) + 850(V-40) = 850 V,
 Simplify: 3 V^2 - 120 V - 34000 = 0,
 
 By quadratic formula,we get V = 20+ 200/3 SQRT(94) = 84.64 mile/hr
 (the speed of the bullet train)
  or 20 - 200/3 SQRT(94) [negative,invalid]
 and so the speed of of the existing train is 44.64 miles/hr

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