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