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Two trains are moving in the opposite direction on parallel tracks
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19 Feb 2021, 06:02
19 Feb 2021, 06:02
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80% (02:52) correct
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Two trains are moving in the opposite direction on parallel tracks at the speeds of 60 km/hr and 90 km/hr respectively. The first train passes a telegraph post in 5 seconds whereas the second train passes the post in 6 seconds. What is the time taken (in seconds) by the trains to cross each other completely?
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Re: Two trains are moving in the opposite direction on parallel tracks
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20 Feb 2021, 10:16
20 Feb 2021, 10:16
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length of train = Speed travelling * time to telegraph post
Calculate length of both trains
Distance to cross each other completely - Sum of distance of both trains --> 1
Since they are travelling in opposite directions = relative speed = Sum of speeds of both trains --> 2
Time = Eq.1/Eq.2
Remember the units.
Calculate length of both trains
Distance to cross each other completely - Sum of distance of both trains --> 1
Since they are travelling in opposite directions = relative speed = Sum of speeds of both trains --> 2
Time = Eq.1/Eq.2
Remember the units.
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: Two trains are moving in the opposite direction on parallel tracks
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20 Feb 2021, 12:10
20 Feb 2021, 12:10
1
OA Explanation:
Speed of Train A = 60 km/hr
Time to cross the post = 5 seconds = \(\frac{5}{3600} = \frac{1}{720}\) hours
Length of Train A = \((60)(\frac{1}{720}) = \frac{1}{12}\) km
Speed of Train B = 90 km/hr
Time to cross the post = 6 seconds = \(\frac{6}{3600} = \frac{1}{600}\) hours
Length of Train A = \((90)(\frac{1}{600}) = \frac{3}{20}\) km
Applying the concept of Relative Velocity:
Total Distance = \(\frac{1}{2} + \frac{3}{20} = \frac{7}{30}\) km
Relative speed = \(60 + 90 = 150\) km/hr
Time taken to cross each other = \(\frac{7}{(30)(150)} = \frac{7}{4500}\) hr
i.e. \((\frac{7}{4500})(3600) = \frac{28}{5} = 5.6\) seconds
Speed of Train A = 60 km/hr
Time to cross the post = 5 seconds = \(\frac{5}{3600} = \frac{1}{720}\) hours
Length of Train A = \((60)(\frac{1}{720}) = \frac{1}{12}\) km
Speed of Train B = 90 km/hr
Time to cross the post = 6 seconds = \(\frac{6}{3600} = \frac{1}{600}\) hours
Length of Train A = \((90)(\frac{1}{600}) = \frac{3}{20}\) km
Applying the concept of Relative Velocity:
Total Distance = \(\frac{1}{2} + \frac{3}{20} = \frac{7}{30}\) km
Relative speed = \(60 + 90 = 150\) km/hr
Time taken to cross each other = \(\frac{7}{(30)(150)} = \frac{7}{4500}\) hr
i.e. \((\frac{7}{4500})(3600) = \frac{28}{5} = 5.6\) seconds
