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
A train is to cover 370 km at a uniform speed. After running 100 km, the train could run at a speed 5 km/h less than its normal speed due to some technical fault. The train got delayed by 36 minutes. What is the normal speed of the train, in km/h?
A train travelling at 36 km/h crosses a pole in 25 seconds. How much time (in seconds) will it take to cross a bridge 250 m long?
A train covers 450 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less to cover the same distance. How much time will it take to cover 315 km at its usual speed?
A train crosses a pole in 12 sec, and a bridge of length 170 m in 36 sec. Then the speed of the train is:
The ratio of the speeds of two trains is 2 : 7. If the first train runs 250 km in 5 hours, then the sum of the speeds (in km/h) of both the trains is:
