Aptitude - Problems on Trains - Discussion

Distance covered in crossing.

When the train crosses a stationary object or pole or another train.
The distance covered by the train = length of the train.

So, the length of the train is 125 m =distance covered by the train.
and we know that it took 10 sec to pass the man.

Train Speed = speed of man*time taken by the train to pass,
Speed = 5km/hr * 10sec.
Speed = 50km/hr.

Given data :

Length Of the Train 125 meters.
Speed of Man = 5 km/hr
Speed of train = ?
Time = 10 sec.

Distance = Time * Velocity (speed).
125 = 10 × v,
V = 125/10,
V = 25/2 M/sec Now Convert it into Km/hr,
V = 25/2 × 18/5,
V = 45 km/hr.

And given In The Question train And Man Is Traveling in Same Direction.
V = Speed of train - Speed Of Man.
45 = Speed of train - 5.
Speed of train = 45+5.
Speed of train = 50 km/hr.

T = L/V1-V2
Where
T = time taken by train to pass the pole
L = Length of the train.
V1 = velocity of the train.
V2= Velocity of the man.
10 = 125/V1-5kmph.
v1-5kmph = 125/10*18/5 (converting m/s into km/h).
V1-5kmph = 45kmph,
V1 = 50kmph.

Let's think man is standing like a pole

125mtrs/10 secs = 12.5 mtrs per sec,
Convert seconds to hours;
12.5 mtrs x 60mins x 60 seconds = 45000 mtrs per hr,
= 45kmph.

The man also moving with some speed right, so the train will take some extra speed to cross than the man

So 45+5 = 50kmph actual train speed.

If we consider man as stationary then the velocity of train is;
Vt=125/10
=12.5 m/s.

Here, the velocity of man is given which is Vm= 5 km/hr.
We have to convert the velocity of the train m/s into km/s.
Then we get,
Vt= 12.5 × 3600/1000 km/hr.
= 45km/hr.
Now, the velocity of the train wrt man.
Vtm= Vt +Vm.
= 45 +5.
= 50 km/hr.

First, let's convert man running speed into second.
5000 ÷ 3600 = 1.38888.
3600 second is equal to 1hr.
1.38888 × 10 second

Why we multiply because we want to know how much the man covered meters in 10 seconds.

So the man covered in 10sec..
Is that 13.88888 then let's multiply.

13.8888×3600 = 50,000 meter
(3,600 is second)

Convert meter into km.
50,000÷1000= 50km.
The answer is 50km train speed.

125 m = 10sec
Than 60sec = 125 x 6 = 750m
1hour = 750 x 60 = 45000m (45km/hr) + 5km/hr = 50km/hr.

@All.

All asking the same doubt "why it is 18/5 and not 5/18"?

It is because the conversion for m/s to km/hr is 18/5 and for km/hr to m/s is 5/18.

How 18/5? Please explain to me.

Step 1:

The relative speed of the train concerning man = Distance/Time =125m/10sec= 12.5m/s.

Step 2: Convert the answer of "step 1" from m/s to km/hr..
To convert it into km/hr multiply it with 18/5.
12.5 * 18/5 = 45km/hr.

Step 3:
Train as well as the man both are moving in the same direction so we will have to subtract the speed of train(x) from the speed of the man(5).
(Note: If the train and man both are moving in opposite directions then add both of their values (x+5) ).

Relative speed = (x-5)km/hr
45km/hr = (x-5),
x=50 km/hr.