A train travelling at a speed of 75 mph enters a tunnel 3 ¹/₂ miles long. The train is ¹/₄ mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

$$\eqalign{ & {\text{Total}}\,{\text{distance}}\,{\text{covered}} \cr & = \left( {\frac{7}{2} + \frac{1}{4}} \right)\,{\text{miles}} \cr & = \frac{{15}}{4}\,{\text{miles}} \cr & \therefore {\text{Time}}\,{\text{taken}} \cr & = \left( {\frac{{15}}{{4 \times 75}}} \right)\,{\text{hrs}} \cr & = \frac{1}{{20}}\,{\text{hrs}} \cr & = \left( {\frac{1}{{20}} \times 60} \right)\,\min \cr & = 3\,\min \cr} $$