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Apr 2808:00 AM PDT
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29 Sep 2009, 11:55
Kudos
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Difficulty:
65%
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Question Stats:
64% (02:08) correct
36%
(02:29)
wrong
based on 630
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Two trains of length 100m and 250m run on parallel lines. when they run in the same direction it will take 70 sec to cross each other and when they run in opposite direction, they take 10 sec to cross each other. Find the speed of faster train.
A. 10 m/s
B. 15 m/s
C. 20 m/s
D. 25 m/s
E. 30 m/s
A. 10 m/s
B. 15 m/s
C. 20 m/s
D. 25 m/s
E. 30 m/s
29 Sep 2009, 13:01
Kudos
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The answer is 20 m/s.
Let the faster train run at x m/s and the slower train run at y m/s.
The first statement states that it will take 70 seconds to cross each other running in the same direction. The first important thing her is that the faster train is behind the slower train, otherwise they would never cross. Secondly, in order to cross the slower train, the faster train will need to cover 350m MORE (250 m + 100 m) in the 70 seconds than the other train.
\(\frac{350}{(x - y)} = 70\)
\(\frac{5}{(x - y)} = 1\)
\(5 = x - y\) (Equation 1)
The second statement states that it will take 10 seconds to cross each other running in the opposite direction. The difference between this and running in the same direction, is that the slower train's speed CONTRIBUTES to the cross rather than inhibiting it. If the slower train was standing still, the faster train would take (350/x) seconds to pass it. Since the slower train is moving in the other direction though, it will take (350/ x+y) seconds to cross.
\(\frac{350}{(x + y)} = 10\)
\(\frac{35}{(x + y)} = 1\)
\(35 = x + y\) (Equation 2)
Solving these two equations, you get x = 20 m/s, and y = 15 m/s.
Let the faster train run at x m/s and the slower train run at y m/s.
The first statement states that it will take 70 seconds to cross each other running in the same direction. The first important thing her is that the faster train is behind the slower train, otherwise they would never cross. Secondly, in order to cross the slower train, the faster train will need to cover 350m MORE (250 m + 100 m) in the 70 seconds than the other train.
\(\frac{350}{(x - y)} = 70\)
\(\frac{5}{(x - y)} = 1\)
\(5 = x - y\) (Equation 1)
The second statement states that it will take 10 seconds to cross each other running in the opposite direction. The difference between this and running in the same direction, is that the slower train's speed CONTRIBUTES to the cross rather than inhibiting it. If the slower train was standing still, the faster train would take (350/x) seconds to pass it. Since the slower train is moving in the other direction though, it will take (350/ x+y) seconds to cross.
\(\frac{350}{(x + y)} = 10\)
\(\frac{35}{(x + y)} = 1\)
\(35 = x + y\) (Equation 2)
Solving these two equations, you get x = 20 m/s, and y = 15 m/s.
manojgmat
Alternative approach:
To cross each other (either in same or opposite direction), the trains have to cover a distance of 250 + 100 = 350 m (the faster train should cover the entire slower train and then its own length so that they completely cross each other)
When they run in the same direction, they cover this distance in 70 sec. So their relative speed in this case (which is the difference in their speeds) is 350/70 = 5 m/s
When they run in opposite directions, they cover this distance in 10 sec. So their relative speed in this case (which is the sum of their speeds) is 350/10 = 35 m/s
If sum if 35 and difference is 5, you should quickly jump to 20 and 15.
Note: We used the concept of relative speed here.
When 2 objects move in same direction, their relative speed i.e. speed relative to each other is the difference of their speeds.
When the 2 objects move in opposite directions, their relative speed i.e. speed relative to each other is the sum of their speeds.
Check this video for when to use relative speed: https://youtu.be/wrYxeZ2WsEM
