Two trains, X and Y, are running on parallel tracks. Train X is 200 m long and travels at 72 km/hr. Train Y is 300 m long. If the trains are traveling in opposite directions, they pass each other completely in 15 seconds. If the trains were traveling in the same direction, how long would it take for the faster train to overtake the slower one?
75 seconds
Convert Train X's speed to metres per second: \(72 \times \frac{5}{18} = 20\) m s-1.
The total length to be crossed when passing is \(200 + 300 = 500\) m.
Moving in opposite directions, relative speed is the sum of the speeds. From the crossing time, relative speed \(= \frac{500}{15} = \frac{100}{3}\) m s-1.
So the sum of the two speeds is \(\frac{100}{3}\), giving Train Y's speed \(= \frac{100}{3} - 20 = \frac{40}{3}\) m s-1.
In the same direction, the relative speed is the difference: \(20 - \frac{40}{3} = \frac{20}{3}\) m s-1.
Time to overtake \(= \frac{500}{\frac{20}{3}} = 500 \times \frac{3}{20} = 75\) seconds.
Hence, the faster train overtakes the slower one in 75 seconds.
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Important Questions from Problem on Trains
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