A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

A. 66 km/hr
B. 72 km/hr
C. 78 km/hr
D. 81 km/hr

• If s is speed of train and x is length of train,
  speed of first person = 4.5 kmph = 4500/3600 = 5/4 mtr per sec = 1.25 mtr per sec
  speed of second person = 5.4 kmph = 5400/3600= 1.5 mtr per sec
  then
  
  x/(s-1.25) = 8.4
  and
  x/(s-1.5) = 8.5
  
  solving it, we get s= 22.5 mtrs per sec
• 12 years agoHelpfull: Yes(10) No(1)
• Let the length of the train be L km and speed be x km/hr
  
  Relative speed when the train overtakes the first person = (x-4.5)km/hr
  Time to overtake the first person = 8.4 sec = 8.4/3600 hour
  L/(x-4.5) = 8.4/3600
  3600L = 8.4x - 37.8 ---(1)
  
  Relative speed when the train overtakes the second person = (x-5.4)km/hr
  Time to overtake the secomd person = 8.5 sec = 8.5/3600 hour
  L/(x-5.4) = 8.5/3600
  3600L = 8.5x - 45.9 ---(2)
  
  8.4x - 37.8 = 8.5x - 45.9
  => .1x = 45.9-37.8 = 8.1
  => x = 81 km/hr
  
  Speed of the train is 81 km/hr
• 7 years agoHelpfull: Yes(1) No(0)