Aptitude - Problems on Trains - Discussion

To convert kilometres per hour (km/hr) to meters per second (m/sec), we use the conversion factor of 5/18. This conversion factor is derived from the relationship between kilometres and meters, as well as hours and seconds.

Here's the breakdown of the conversion:

1 kilometer = 1000 meters.
1 hour = 3600 seconds.

To convert km/hr to m/sec, we need to cancel out the kilometres and hours units while retaining the meters and seconds units. We can do this by multiplying the value in km/hr by a conversion factor that equates to 1.

To convert kilometres to meters, we multiply by 1000 (since 1 kilometre is equal to 1000 meters). This step cancels out the kilometres unit.

To convert hours to seconds, we multiply by 3600 (since 1 hour is equal to 3600 seconds). This step cancels out the hours unit.

So, the conversion factor becomes:
(1000 meters/1 kilometer) * (1 hour/3600 seconds)

Simplifying this expression gives us:
(1000/1) * (1/3600) = 1000/3600 = 5/18.

Hence, multiplying the value in km/hr by 5/18 will convert it to m/sec.

Why we are multiplying the 60 with 5/18?

The answer is simple. We are converting the 'kilo-meters/hour' value into 'meters/second'.

Let me explain about converting km/hr into m/s in detail.

1 km = 1000 meters.
1 hr = 3600 seconds.

1 km/hr = 1000/3600 m/s

= 10/36 m/s

= 5/18 m/s.

Therefore 1 km/hr = 5/18 m/sec.

Similarly 60 km/hr = 60 x 5/18 m/sec.

You may ask me, why should I convert it from km/hr to m/sec?

Because, the time taken by the train is given in terms of seconds (9 seconds) and the 4 options are in terms of metres. But the speed of the train is given in terms of km/hr. So we have to convert the values from km/hr to m/s in order to find the solution in terms of metres/seconds.

Hope you understand better. Have a nice day guys!

Given:
1. Length of the train = 130 m
2. Speed of the train = 45 km/hr or (25/2) m/s
3. Time taken by the train to cross bridge = 30s

Find:
Length of the bridge = x meter

First, convert speed of the train from km/hr into m/s
So, speed of the train in m/s = [45*(5/18)] km/hr = (25/2) m/s

Now,
Distance(or length) = speed * time

But,Distance = (Length of the bridge + Length of the train) = speed * time
Distance = x + 130 = (25/2) * 30

x+130 = 375
x = 375 - 130
Length of the bridge = 245 m

To find the length of the bridge, we need to calculate the distance the train travels in 30 seconds.

First, we convert the train's speed from km/hr to m/s:

Speed in m/s = (Speed in km/hr * 1000)/3600
So, the train's speed in m/s = (45 km/hr * 1000)/3600 = 12.5 m/s.

Now we can calculate the distance the train travels in 30 seconds:
Distance = Speed * Time.

Distance = 12.5 m/s * 30 s = 375 meters.

Since the train is 130 meters long, the remaining distance must be the length of the bridge:
Length of the bridge = Distance - Length of the train.

Length of the bridge = 375 m - 130 m = 245 meters.

Therefore, the length of the bridge is 245 meters.

HI All,

Let's simplify this:

Distance traveled(d) = speed(d) * time(t) taken to travel that distance(d)

Speed is 45km/h.
Since answer needs to be in meter, let's convert Km/h into m/sec.

so, 45*(1000/3600), because 1km=1000mtr and 1hr= 3600sec(60minutes*60 sec per minute).

So, our m/sec speed(s) comes to be 45*(5/18)=25/2mtr per sec.
We have s = 25/2m/sec and t= 30 secs. so d = s*t =375mtr.

Since train itself is 130mtr long it wouldn't travel all 375mtr. So, the distance actually traveled(bridge length)by train is 375mtr- 130mtr = 245mtr.

hope this helps.

Formula given in important formulas section as:

Time taken by a train of length l metres to pass a stationery object of length b metres is the time taken by the train to cover (l+b) metres.

In the problem given train length l = 130 m.

Since bridge can be considered as a stationary object of length b.

Time for train to cross bridge is 30 s.

So by the given formula time to cross the bridge (stationary object of length b) = l+b.

30 = l+b.

=> 30 = 130+b.

b = 100.

Any body please help me why this is wrong?

Length of the train l1 = 130m;
Speed s = 45kmph;
time t = 30 sec ;
length of the bridge l2 = ?

Here total distance D= (length of the train + length of the bridge)
so d=l1+l2;
we know the formula of distance (d)=speed(s)*time(t);
but the speed in kmph we have to convert into mph so speed (s) = 45*(5/18)=25/2;
then d=s*t;
then substitute all the values in it.
(l1+l2)=(25/2)*30;
we know the l1 value l1=130m;
(130+l2)=(25*15)
(130+l2)=375
then l2 =375-130
length of the bridge is l2=245;

The length of the train is=130 m.
Lets assume the length of the bridge = x m.

In 30 sec the train traveled a distance of = (x+130)m.
Therefore the speed of the train = (x+130)/30 m/sec.

The speed of the train = 45 kmph.(Which is already given).
Therefore 45 kmph= (x+130)/30 m/sec.
Convert the 45 kmph into m/sec.

Then,

45* 1000/3600 = (130+x)/30.
45 * 100/ 12 = 130+x.
15 *25 = 130+x.
375 = 130+x.
==> x= 375-130= 245 m.
Therefore the the length of the bridge is 245 m.

We have to calculate speed.

Speed = 45*5/18=25/2 m/s.

Time is given t= 30 sec.
Let's find the length of the bridge,
Let the length of the bridge is X.

And whenever a train crosses the bridge then the total distance covered by the train is the length of the bridge it's own length (train's length).

According to the motion's 1st law distance or displacement = speed * time.
X + 130 = 25/2 * 30.
2(X + 130) =750.
2X + 260 = 750.
X = (750-260)/2= 245m.

THE SIMPLEST WAY OF SOLVING THIS PROBLEM

train speed=45km/hr=>45*(5/18)=25/2 m/sec;

25/2 m/sec means

the train can travel a distance of 25/2 meters in 1 sec

1 sec--->25/2mts
30sec--->(25/2)*30=>375meters

therefore the total distance covered by the train in 30 seconds is 375 meters(i,e train length+bridge length)

by subtracting the train length from the total distance we can find out the length of the bridge i,e
375-130=245 meters