Discussion
Two trains are moving in the same direction at 50 km/h and 30 km/h. The faster train crosses a man in the slower train in 18 seconds. Find the length of the faster train.
Answer: A
The faster train is 100 m long.
The trains move in the same direction, so the faster train passes the man at the difference of their speeds. In crossing him, it covers its own length.
\[ \begin{aligned} v &= 50 - 30 = 20 \text{ km/h} \\ &= 20 \times \frac{5}{18} = \frac{50}{9} \text{ m/s} \\ L &= \frac{50}{9} \times 18 = 100 \text{ m} \end{aligned} \]
Using the sum of the speeds (80 km/h), as for trains moving in opposite directions, would give 400 m, which is not offered. 120 m, 90 m and 150 m do not fit a relative speed of 20 km/h over 18 seconds.
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