A man walks with 3 kmph speed in the direction of a train. How much time will a 500 m long train take to overtake him at a speed of 63 kmph?

Sure, let's solve this step by step:

Step 1: Convert all speeds to the same unit. Here, the speed of the man is given in km/h and the length of the train is given in meters. So, let's convert the speed of the train from km/h to m/s by multiplying it by 5/18.

So, the speed of the train = 63 km/h * 5/18 = 17.5 m/s

Step 2: The man is moving in the same direction as the train, so the relative speed of the train with respect to the man is the difference of their speeds.

So, the relative speed = Speed of train - Speed of man = 17.5 m/s - (3 km/h * 5/18) = 17.5 m/s - 0.83 m/s = 16.67 m/s

Step 3: The time it takes for the train to overtake the man is the length of the train divided by the relative speed.

So, Time = Length of train / Relative speed = 500 m / 16.67 m/s = 30 seconds

So, the train will take 30 seconds to overtake the man.