# Problems on trains

__Problems on trains__

There are train based problem based on two object, First is Train and second object is that which is crossed by the train.

__Some important Facts__

If a train moving or cross a pole or man than the first object is train and the second object is pole or man.

- If the train moving or cross the platform than the first object is train and second object is platform which is train cross.

- If a train cross or moving a man who is standing on platform than the train is first object and the second object is man.

- When a train crossing or moving another train in the same direction or opposite direction than the first object is first train and second object is second train.

__Example:__

A train having length 250 meters, passes a poll in 5 seconds. How long will it take to cross a bridge 500 meters long?

__Answer:__

We know the speed of train = 250 meters .

(250/ 5) m / sec = 50m / sec

**Time taken to cross the bridge = (500 / 50) m / sec = 10m / sec **

__Example:__

A super fast train 150m long is running at the speed 90 Km / hr. Find the time taken by it to pass a boy standing near the railway track.

__Answer:__

After converting the speed of super fast train Km / hr to m / sec

So, (90 x 5 / 18) m / sec = 25 m / sec.

The super fast train passing a standing boy near the railway track = 150 m.

So, The time taken to cross the standing boy is T = D / S = (150 / 25) sec = 6 sec

__Example:__

A Rajdhani Express train 160m long and running at speed 72 Km / h. It crosses a platform which is 240 m long .How much time will it cross a platform.

__Answer:__

The length of train and platform is 160m + 240m = 400m,

Speed = (72 x 5)/ 18 = 20 m / sec.

Required time to cross a platform is T = D / S, = 400 / 20 = 20 sec.

__Example:__

In what time will a 350 meter long train running at the speed of 90 km / hr cross a pole ?

__Answer:__

Speed= 90 x 5 / 18 = 25 m / s

**Time = 350 / 25 = 14 seconds **

__Problem on speed taken by train__

__Example:__

A 150 m long train takes 30 seconds to cross a man standing on a platform, The speed of the train is :

__Answer:__

We know the formula Speed = Distance / Time

So , Distance = 150 m , Time = 30 Seconds

Speed = ( 150 / 30 ) m / sec = 5 m / sec .

**speed of the train is 5 m / sec .**

__Example:__

A women on holiday travel first 140 km at 75 km / hr and the next 140 km at 75 km / hr . The average speed for 280 km of the tour is

__Answer:__

women taking total time to travel is = ( 140 / 75 + 140 / 75 ) = 28 / 5 hrs

**Average speed = ( 280 x 5 / 28 ) = 50 km / hr.**

__Example:__

A train 165 meters long crosses a electric poll in 5 seconds. The speed of the trains in km /hr is-

__Answer:__

Speed = Distance / Time

So , Distance = 165 m , Time = 5 Seconds

Speed = ( 165 / 5 ) m / sec = 33 m / sec .

Convert m / sec into km / hr (18 / 5) km /hr

33 x 18 / 5 = 594 / 5 = 118.8 km / hr

**speed of the train is 118.8 km / hr **

__Example:__

A slow Local train whose length is 150 meter long and a bridge length is 550 meter to cross the bridge by local train in 50 sec, Then find the speed of train to crossing a bridge.

__Answer:__

The length of both train and bridge that is 150 + 550 = 700 meter, and we know the formula of speed = Distance / Time , So 700 / 50 = 14 meter / sec.

__Example:__

A boy is standing on a railway bridge and which is 150 m long. He found that a train passes the bridge in 40 seconds but the train himself in 10 sec, Find the length of the train and speed.

__Answer:__

First we find the length of train, the we assume that length of train be L meters.

then, L / 10 = L + 150 / 40 = 40 L = 10L + 1500 ,

so, L = 50 meter. and now speed of train is D / T = 50 / 10 = 5 m / sec . and now convert it into 5 x 18 / 5 = 18 Km / hr.

**So speed of train is 18 Km / hr.**

__Problem on Train running same direction__

__Example:__

A train is 250 meter long is running of **speed 65 Km / hr,** A man running at **5 Km / hr i**n **same direction** in which the train is moving, find the what **time** will it pass a man .

__Answer:__**If direction is given in the same direction then we subtract it ( 65 – 5 ) = 60 Km /hr.**

and now convert it into **m / sec** using **60 x 5 / 18 = 50 / 3 m / sec.**If the train time taken to passing the man who running , that is **50 / 3 m /sec**. So we can easily get the distance of m / sec so it **cover 250 meter** that is = **250 x 3 / 50 = 15 sec **

So, the train time taking to cover distance is **15 sec.**

__Example:__

Two super fast train 180 meters and 180 meters in length respectively are running in same directions , one at the rate of 58 km and the other at the rate of 50 km an hours . What time will they be completely clear of each other?

__Answer:__

Two fast trains are running is same direction and their relative speed is = 58 – 50 = 8 km / hours .

8 x 5 / 18 = 20 / 9 m / sec .

Total length of both train is ( 180 + 180 ) = 360 meters .

**So , the required time is =** Total length / Relative speed = 180 + 180 / 30 = 360 x 9 / 20 = 162 sec

__Problem on train running opposite direction__

__Example:__

Two super fast train 180 meters and 180 meters in length respectively are running in opposite directions , one at the rate of 58 km and the other at the rate of 50 km an hours . What time will they be completely clear of each other from the moment they meet

__Answer:__

Two fast trains are running is opposite direction and their relative speed is = 58+50 = 108 km / hours .

So the two trains are each other meet at 108 km /hours

108 x 5 / 18 = 30 m / sec

**So, the required time is =** Total length / Relative speed = 180 + 180 / 30 = 12 sec

__Problem on finding length of train or platform__

__Example:__

A Express train is running at speed of 90 Km / hr. It crosses a bridge whose length is twice that of train in 36 seconds. What is the length of bridge in meter?

__Answer:__

At First we convert the speed into 90 Km / hr = 90 x 5/18 = 25 m /sec.

now here is suppose the train length is x so bridge length is 2x.

according to question

25 = x + 2x / 36

x = 300 m .

length of platform is 300 x 2 = 600 m.

**So length of bridge is 600 meter.**

__Example:__

A metro rail is running at speed of 90 km / hr . If crosses a platform whose length is twice that of train in 36 seconds. What is the length of platform in meter?

__Answer:__

Speed = 90 x 5 / 18 = 25 m / s .

25 = x + 2x / 36

x = 300 meter

**Length of platform = 300 x 2 = 600 meter.**

__Example:__

A express train passes a tunnel in 21 sec whose length is 130 m long moving with speed of 90Km / hr. what is the length of tunnel ?

__Answer:__

Let length be the x meters.

We know the conversion of Km/hr to m/sec is = 90 x 5 / 18 = 25 m/sec

25 = 130 + x / 21

130 + x = 25 x 21

x = 525 – 130

x = 395

**so length be the 395 meters.**