A train $150$ m long, travelling at $75$ km per hour overtakes another train travelling in the same direction at $45$ km per hour. In how many seconds does the first train pass a passenger sitting in the second train?

Since both trains move in the same direction, the relative speed is $75-45=30$ km/hr. Convert this to m/s: $30\times \frac{5}{18}=\frac{25}{3}$ m/s. The first train has to cover only its own length, $150$ m, relative to the passenger. Thus time $=\frac{150}{25/3}=18$ s.