A train traveling at 48 kmph completely crosses another train having half its length and traveling in the opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
Question
A train traveling at 48 kmph completely crosses another train having half its length and traveling in the opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
Solution
To solve this problem, we first need to find the length of the train.
Step 1: Find the relative speed of the two trains. Since they are moving in opposite directions, we add their speeds. Convert the speed from km/h to m/s by multiplying by 5/18.
Relative speed = (48 + 42) * (5/18) = 50 m/s
Step 2: The time it takes for the trains to cross each other is 12 seconds. The length of the train is the relative speed times the time.
Length of the train = Speed * Time = 50 m/s * 12 s = 600 m
Step 3: The length of the second train is half the length of the first train, so it is 600 m / 2 = 300 m.
Step 4: The time it takes for the first train to cross a platform is 45 seconds. The distance it covers in this time is its own length plus the length of the platform.
Let's denote the length of the platform as P.
So, Speed * Time = Length of the train + Length of the platform
48 * (5/18) * 45 = 600 + P
P = 48 * (5/18) * 45 - 600 = 300 m
So, the length of the platform is 300 meters.
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