Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

$$\eqalign{ & {\text{Relative}}\,{\text{speed}} \cr & = \left( {45 + 30} \right)\,{\text{km/hr}} \cr & = \left(75 \times \frac{5}{18} \right)\, \text{m/sec} \cr & = {\frac{{125}}{6}} \,{\text{m/sec}} \cr & {\text{We}}\,{\text{have}}\,{\text{to}}\,{\text{find}}\,{\text{the}}\,{\text{time}}\,{\text{taken}}\,{\text{by}}\,{\text{the}} \cr & {\text{slower}}\,{\text{train}}\,{\text{to}}\,{\text{pass}}\,{\text{the}}\,{\text{DRIVER}}\,{\text{of}}\, \cr & {\text{The}}\,{\text{faster}}\,{\text{train}}\,{\text{and}}\,{\text{not}}\,{\text{the}}\,{\text{complete}}\,{\text{train}}{\text{.}} \cr & \cr & {\text{So,}}\,{\text{distance}}\,{\text{covered = Length}}\,{\text{of}}\,{\text{the}}\,{\text{slower}}\,{\text{train}}. \cr & {\text{Therefore,}}\,{\text{Distance}}\,{\text{covered = 500}}\,{\text{m}}. \cr & \therefore {\text{Required}}\,{\text{time}} \cr & = {500 \times \frac{6}{{125}}} \cr & = 24\,\sec \cr} $$