Discussion
From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?
Answer: D
The train is 175 m long and the platform 200 m.
54 km/h is 15 m/s and 9 km/h is 2.5 m/s. Passing the man, the train covers its own length at the relative speed:
\[ \begin{aligned} \text{train} &= (15 - 2.5) \times 14 = 175\ \text{m} \\ \text{train + platform} &= 15 \times 25 = 375\ \text{m} \\ \text{platform} &= 375 - 175 = 200\ \text{m} \end{aligned} \]
210 and 140 come from ignoring the man's speed (15 × 14 = 210). The other pairs add up to 375 or less but give a train length that does not match the 14 seconds at the relative speed.
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