# Problems on Trains

A train moves with a speed of 108 kmph. its speed in metres per second is :

108 kmph = $$\left ( 108 \times \frac{5}{18} \right )$$ m/sec = 30 m/sec

A speed of 14 metres per second is the same as :

14 m/sec = $$\left ( 14 \times \frac{18}{5} \right )$$ km/hr = 50.4 km/hr

In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr ?

Speed = $$\left ( 144 \times \frac{5}{18} \right )$$ m/sec = 40 m/sec

∴ Time taken = $$\frac{100}{40}$$ sec = 2.5 sec

A train 280 m long, running with a speed of 63 km/hr will pass a tree in :

Speed = $$\left ( 63 \times \frac{5}{18} \right )$$ m/sec = $$\frac{35}{2}$$ m/sec

∴ Time taken = $$280 \times \frac{2}{35}$$ sec = 16 sec

How long does a train 110 metres long running at the speed of 72 km/hr take to cross a bridge 132 metres in length ?

Speed = $$\left ( 72 \times \frac{5}{18} \right )$$ m/sec = 20 m/sec

Total distance covered = (110 + 132) m = 242 m

∴ Required time = $$\frac{242}{20}$$ sec = 12.1 sec

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is :

Speed = $$\left ( 45 \times \frac{5}{18} \right )$$ m/sec = $$\frac{25}{2}$$ m/sec; Time = 30 sec

Let the length of bridge be x metres.

Then, $$\frac{130 + x}{30} = \frac{25}{2}$$

⇒ 2(130 + x) = 750

x = 245 m

A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is :

Speed = $$\left ( 78 \times \frac{5}{18} \right )$$ m/sec = $$\frac{65}{3}$$ m/sec

Time = 1 minute = 60 seconds.

Let the length of the tunnel be x metres.

Then, $$\frac{800 + x}{60} = \frac{65}{3}$$

⇒ 3(800 + x) = 3900

x = 500.

A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train ?

Speed = $$\left ( 72 \times \frac{5}{18} \right )$$ m/sec = = 20 m/sec

Time = 26 sec.

Let the length of the train be x metres.

Then, $$\frac{x + 250}{26} = 20$$

x + 250 = 520

x = 270.

The length of a train and that of a platform are equal. If with a speed of 90 km/hr ,the train crosses the platform in one minute, then the length of the train (in metres) is:

Speed = $$\left ( 90 \times \frac{5}{18} \right )$$ m/sec = = 25 m/sec

Time = 1 min. = 60 sec.

Let the length of the train and that of the platform be x metres.

Then, $$\frac{2x}{60} = 25$$

⇒ $$x = \frac{25 \times 60}{2} = 750$$

A train of length 150 metres takes 40.5 seconds to cross a tunnel of length 300 metres. What is the speed of the train in km/hr ?

Speed = $$\frac{150 + 300}{40.5}$$ m/sec

= $$\left ( \frac{450}{45.5} \times \frac{18}{5} \right )$$ km/hr

= 40 km/hr