A train passes two persons walking in the same direction in which the train is going. These persons are walking at the rates of 2 km/hr and 4 km/hr, respectively, and are completely crossed by the train in 9 seconds and 10 seconds, respectively. What is the length of the train?
50 meters
Let the speed of the train be \(v\) km/h and its length be \(L\) metres.
Since the persons walk in the same direction as the train, the relative speed with the first person is \((v - 2)\) km/h, and with the second person is \((v - 4)\) km/h.
Using \(L = (v-2) \times \frac{5}{18} \times 9\) and \(L = (v-4) \times \frac{5}{18} \times 10\), equate both: \((v-2) \times 9 = (v-4) \times 10\).
\(9v - 18 = 10v - 40 \Rightarrow v = 22\) km/h.
So \(L = (22-2) \times \frac{5}{18} \times 9 = 20 \times \frac{5}{18} \times 9 = 50\) metres.
Hence, the length of the train is 50 metres.
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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:
