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
Eight railway stations A, B, C, D, E, F, G and H are connected either by two-way passages or one-way passages. One-way passages are from C to A, E to G, B to F, D to H, G to C, E to C and H to G. Two-way passages are between A and E, G and B, F and D, and E and D.
If the route between G and C is closed, which one of the following stations need not be passed through while travelling from H to C?
A daily train is to be introduced between station A and station B starting from each end at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the Shuttle Service?
A train with a uniform speed passes a 122 meters long platform in 17 seconds and a 210 meters long bridge in 25 seconds. The speed of the train is:
How long does a train 153 meters long running at the rate of 90 kmph take to cross a bridge 622 meters in length?
A train passes a 360 metre long platform in 40 seconds and a man standing on the platform in 16 seconds. The speed of the train is:
