An express train takes 1 hour less than a passenger train to travel 132 km between two stations. If the average speed of the express train is 11 km/hr more than that of the passenger train. Find the average speed of the two trains ?

• if we take avg speed of passanger train as 'x'kmph
  then the avg speed of express train is '(x+11)'kmph
  it's given that the time difference between 2 trains is 1hr
  i.e., 132/x - 132/(x+11) = 1
  solving above eqn we get x=33
  so,
  speed of the passenger train will be 33 kmph
  and, speed of the express train will be 33 + 11 = 44 km
  therefore, average speed of trains are,
  [33+44]/2=38.5kmph
• 12 years agoHelpfull: Yes(19) No(1)
• answer 33.44
  
  let the ordinary train takes x hours the time taken by express train is x-1
  
  speed of ordinary train = 132/x
  
  speed 0f express train =132/x-1
  
  given 132/x-1 =132/x +11
  
  simplifying x²-x-12=0
  
  (x-4)(x+3)=0
  
  x=4. speed of ordinary train =132/4 =33
  
  speed of express train =33+11=44
• 12 years agoHelpfull: Yes(5) No(1)
• 44km/h.
  
  Let the average speed of passenger train = X km/h.
  Average speed of express train = (X + 11) km/h
  
  We know that the time taken by the express train to cover 132 km is 1 hour less than the passenger train to cover the same distance.
  
  Therefore,
  132/X - 132/(X+11) = 1
  
  --> 132[(X+11-X)/(X(X+11)] =1
  --> 132 *11/X(X+11) =1
  --> 132 *11 = X(X+11)
  --> X^2 + 11X -1452 = 0
  --> X^2 + 44X - 33X - 1452 = 0
  --> X(X+44) - 33(X+44) = 0
  --> (X+44)(X-33) =0
  --> X = -44, X=33
  
  Speed cannot be negative.
  Therefore, the speed of the passenger train will be 33 km/h and
  Thus, the speed of the express train will be 33 + 11 = 44 km/h.
• 12 years agoHelpfull: Yes(4) No(1)
• Let the time taken by passenger train be x hrs [1]
  and thus by express train will be (x-1) hrs
  
  Let the speed of passenger train be y km/h [2]
  and that of express train be (y+11) km/h
  
  we know distance= 132km
  
  since speed = distance/time
  therefore for passenger train : y= 132/x ( from [1] and [2])
  : xy=132 [3]
  
  similarly for express train : y+11 = 132/(x-1)
  : xy-y+11x=143
  Since xy=132 by [3]
  
  thus 132-y+11x =143
  i.e -y+11x=11
  Since y= 132/x
  
  thus -(132/x) + 11x= 11
  this gives us x=1,12
  
  x can not be 1, so x= time by passenger train= 12hrs
  this y= avg speed of passenger train = 132/12 (dst/time) = 11km/hr
• 12 years agoHelpfull: Yes(0) No(9)