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Problems on Trains

1.

Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?

Let the speed of the slower train be x m/sec.

Then, speed of the train = 2x m/sec.

Relative speed =  ( x + 2x) = 3x m/sec.

(100 + 100)/8 = 3x => x = 25/3.

So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.

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2.

Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?

Relative speed = (40 - 20) = 20 km/hr.

= 20 * 5/ 18 = 50/9 m/sec.

Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.

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3.

How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

Speed of train relative to man = 63 - 3 = 60 km/hr.

= 60 * 5/18 = 50/3 m/sec.

Time taken to pass the man = 500 * 3/50 = 30 sec.

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4.

A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?

Let the length of the train be x m and its speed be y m/sec.

Then, x/y = 8 => x = 8y

(x + 264)/20 = y

y = 22

Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.

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5.

A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?

Let the length of the train be x m and its speed be y m/sec.

Then, x/y = 15 => y = x/15

(x + 100)/25 = x/15 => x = 150 m.