A train 125 metres long passes a man in 10 seconds running at 5 km/hour in the same direction as the train. What is the speed of the train?

Given:

Length of the train = 125 metres

Time taken to pass the man = 10 seconds

Speed of the man = 5 km/hour

Formula Used:

Relative speed = (Length of the train) / (Time taken to pass the man)

Speed of the train = Relative speed + Speed of the man

Calculation:

First, we convert the speed of the man to m/s:

Speed of the man = 5 km/hour = \(5 × \frac{1000}{3600}\)

Speed of the man = \(\frac{5000}{3600}\) m/s

Speed of the man = \(\frac{25}{18}\) m/s

Next, calculate the relative speed:

Relative speed = \(\frac{Length of the train}{Time taken to pass the man}\)

Relative speed = \(\frac{125}{10}\) m/s

Relative speed = 12.5 m/s

Now, convert the relative speed to km/h:

Relative speed = \(12.5 × \frac{3600}{1000}\)

Relative speed = 45 km/h

Finally, calculate the speed of the train:

Speed of the train = Relative speed + Speed of the man

Speed of the train = 45 + 5

Speed of the train = 50 km/h

The speed of the train is 50 km/h.