Discussion
A train 450m long takes 45s to cross a man running at a speed of 8 km/h in the same direction as that of the train. What is the speed of the train?
Answer: C
The train's speed is 44 km/h. The train covers its own length of 450 m in 45 s relative to the man, so the relative speed is 450 / 45 = 10 m/s, which is 36 km/h.
\[ 10 \times \frac{18}{5} = 36 \text{ km/h} \]\[ 36 + 8 = 44 \text{ km/h} \]They move in the same direction, so the man's speed is added to the relative speed to get the train's speed; 42, 43 and 45 do not satisfy this.
Check: a train at 44 km/h and a man running at 8 km/h in the same direction are 36 km/h apart, which is 10 m/s, and the train's 450 m take 45 s to pass him. If the man were running against the train the speeds would be added instead, and the train would then be 28 km/h, which is not an option.
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