Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?

$$\eqalign{ & {\text{Relative}}\,{\text{speed}} = \left( {40 - 20} \right)\,{\text{km/hr}} \cr & = \left( {20 \times \frac{5}{{18}}} \right)\,{\text{m/sec}} \cr & = {\frac{{50}}{9}} \,{\text{m/sec}} \cr & \therefore {\text{Length}}\,{\text{of}}\,{\text{faster}}\,{\text{train}} \cr & = \left( {\frac{{50}}{9} \times 5} \right)\,m \cr & = \frac{{250}}{9}\,m \cr & = 27\frac{7}{9}\,m \cr} $$