Aptitude - Problems on Trains - Discussion

We know that 1 kilometre = 1000 meters and 1 hour = 3600 seconds.
Now, 1 km/h can also be written as 1000/3600: 1 (kilometre/hour) = 1000/3600 (meters/seconds).
So, this is the formula which is used to convert km/h to m/s.
On simplifying 1000/3600 further, we get 5/18.

1 km = 1000 meter.
and 1 hrs= 3600 sec.

So converting it in mtr/sec= 1000/3600.
So, you will get 5/18.

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!

First convert the unit km/hr into m/s, because the length of the train is given in meters.

->so ,1km=1000m and 1 hr=1*60*60=3600 secs.

Now ,as we all know, the formula for speed in terms of distance is
speed =distance /time.
=>(60*1000/3600) m/s = distance/9 secs.
=>60*5/18 = length of train/9(time taken to cross the pole by train)
=>9*60*5/18 = length of the train.
=>length of the train =150 m.

Given Time = 9 sec,
Covert Speed km/hr to m/sec.
1 km = 1000m,
1 hr = 60 min,
1 min = 60 sec.
60 min=(60 * 60) sec = 3600 sec.
So, 1 hr = 3600 sec.
1 hr = 3600 sec.

1 km/hr = 1km/1hr = 1000 m/3600 sec = 10/36 m/s = 5/18 m/s,
Speed = 60 km/hr = 60 * 5/18 m/s,
Speed = Distance/Time.
So, the Length of the train = Speed * Time
= 60 * 5/18*9
= 150m.

Thanks all for explaining it.

How come 5/18? Please explain me.

Speed = distance/time or velocity = distance/time or s = s/t.

Distance = speed*time.
= 60km/hr*9sec.
= 60(1km=1000m/1hr=3600sec)*9sec
(i.e. 1km = 1000m , 1hr = 60min, 1min = 60sec)

Sso 1hr = 60min*60sec.
= 60(1000m/3600sec)*9sec
= 60(10/36m/sec)*9sec,
= 60(0.277m/sec)*9sec,
= 60(2.493m),
= 149.58m = 150m answer.

What is a pole?
In this problem, a “pole” is just a single post or point beside the railway track.
Distance covered by the train while crossing the pole = length of the train.

Formula:
Speed = Distance/Time.
And Distance = Speed × Time.

Convert km/hr into meters per second (m/s):
NOTE: 1 km/hr = 1×(5/18) m/s
60 km/hr = 60×(5/18) = 300/18 m/s
Multiply by time to get distance (length of the train): Distance = (300/18)×9 = 150 meters,
Answer: The length of the train = 150 meters.

Simplest way,

Our train took 9 secs at 60 kmph.
Convert the time taken into hours ->. 0025 hrs.
So, distance (required length) = Speed x Time = 60 x. 0025 =. 15 km = 150 m.