A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Question
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Solution
Sure, let's solve this step by step:
Step 1: Convert the speed of the train from km/hr to m/s. We know that 1 km/hr = 5/18 m/s. So, the speed of the train is 54 * 5/18 = 15 m/s.
Step 2: Calculate the length of the train. The train passes a man standing on the platform in 20 seconds. We know that speed = distance/time. So, the length of the train (which is the distance in this case) is speed * time = 15 m/s * 20 s = 300 m.
Step 3: Calculate the time it takes for the train to pass the platform. We know that the train passes the platform in 36 seconds.
Step 4: Calculate the length of the platform. The train and the platform together take 36 seconds to pass. So, the length of the train + the length of the platform = speed * time = 15 m/s * 36 s = 540 m.
Step 5: Subtract the length of the train from the total length to get the length of the platform. So, the length of the platform = 540 m - 300 m = 240 m.
So, the length of the platform is 240 meters.
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