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?
The length of a train and that of a platform are equal. If with a speed of 108 km/hr the train crosses the platform in one minute. Then the length of the train (in metres) is:
A train can cross a pole and a bridge 75 meters long in 10 seconds and 25 seconds respectively. Find the length of the train.
A 275 metre long train crosses a platform of equal length in 33 seconds. What is the speed of the train in kmph?
