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September 26th, 2018, 08:30 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 470 Thanks: 1  I got three different answers for this problem
The ratio of the speeds of a goods train and a passenger train is 3:7. The two trains can cross each other in 40 sec. A man on the passenger train observes that the goods train crosses him in 25 seconds. If the goods train is 275m long, what is the length of the passenger train? A) First method: Crossing each other means travelling in opposite direction: (275 + X)/275 = 40/25 = 8/5 It can written as (5+3)/5 = (275 + X)/275 Here 5 corresponds to 275 3 corresponds to 275/5*3 = 165 Second method: Total distance = 275 + X X means length of passenger train. Relative speed = either 7 + 3 = 10 (or) 7  3 = 4. There are 2 relative speed values because they didn’t mention whether trains are approaching each other or moving in other direction: Time = (Distance )/speed 40 sec = (275 + X)/10 or (275 + X)/4 X = 400 – 275 (or) 160 – 275 = 125 (or)  115 Which is the correct one? Last edited by skipjack; September 27th, 2018 at 12:55 PM. Reason: to correct typos 
September 27th, 2018, 12:12 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Last edited by Denis; September 27th, 2018 at 12:42 PM. 
September 27th, 2018, 01:10 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,972 Thanks: 2222 
The first method is correct. The second method is incorrect. The trains' directions are irrelevant. If u m/s is the relative speed, 40 = (275 + X)/u. You didn't use the man's observation, which gives 25 = 275/u, so u = 11. Hence X = 165. 
September 27th, 2018, 01:15 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  

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