When my friend, Prof. Rajesh Sadagopan was travelling to Bangalore, he found that his train, which was moving uniformly, passed a telegraph post in 14 seconds and a platform 210 m long in 42 seconds. Find the length of the train.
Question
When my friend, Prof. Rajesh Sadagopan was travelling to Bangalore, he found that his train, which was moving uniformly, passed a telegraph post in 14 seconds and a platform 210 m long in 42 seconds. Find the length of the train.
Solution
Sure, let's solve this step by step.
Step 1: First, we need to understand that when the train crosses a telegraph post, the distance covered is equal to the length of the train. Let's denote the length of the train as 'L' and the speed of the train as 'S'. So, from the problem, we know that the train crosses the telegraph post in 14 seconds. Therefore, we can write the equation as:
L = S * 14 ---- (Equation 1)
Step 2: When the train crosses a platform, the distance covered is equal to the length of the train plus the length of the platform. From the problem, we know that the length of the platform is 210 m and the train takes 42 seconds to cross it. So, we can write the equation as:
L + 210 = S * 42 ---- (Equation 2)
Step 3: Now, we have two equations with two variables (L and S). We can solve these equations simultaneously to find the values of L and S.
Subtract Equation 1 from Equation 2, we get:
210 = S * 42 - S * 14 210 = S * (42 - 14) 210 = S * 28
So, S = 210 / 28 = 7.5 m/s
Step 4: Substitute S = 7.5 m/s into Equation 1, we get:
L = 7.5 * 14 = 105 m
So, the length of the train is 105 m.
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The correct answer is: The train takes 3 seconds to pass the signal post. See the diagram below that shows the motion of the train. The star shows the front (engine) of the train.The time of passing starts from time T2T 2 and lasts till time T3T 3 . Let this time be = T3T 3 - T2T 2 = T seconds.Then the distance moved by the engine (star on the train) during the passing time is = 20 m/s ×× T seconds = 20T metersBut from the diagram it is clear that this distance is the length of the train = 60 meters. So: 20 ×× T = 60 ⇒⇒ T = 3 seconds.
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