A train 250m long takes 30s to cross a man running at a speed of 6km/h in the direction opposite to that of train. What is the speed of the train?
Question
A train 250m long takes 30s to cross a man running at a speed of 6km/h in the direction opposite to that of train. What is the speed of the train?
Solution
Sure, let's solve this step by step:
Step 1: Convert the speed of the man from km/h to m/s. We know that 1 km/h = 5/18 m/s. So, the speed of the man = 6 km/h = 6 * (5/18) m/s = 5/3 m/s.
Step 2: The train crosses the man in 30 seconds. This means the relative speed of the train to the man is the length of the train divided by the time taken to cross, which is 250m / 30s = 8.33 m/s.
Step 3: The relative speed is the sum of the speeds of the train and the man because they are moving in opposite directions. So, the speed of the train = relative speed + speed of the man = 8.33 m/s + 5/3 m/s = 10 m/s.
Step 4: Convert the speed of the train from m/s to km/h. We know that 1 m/s = 18/5 km/h. So, the speed of the train = 10 m/s = 10 * (18/5) km/h = 36 km/h.
So, the speed of the train is 36 km/h.
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