Aptitude - Problems on Trains - Discussion

We 1st Find the speed of train relative to man Vr.
Man and train moved in the same direction = (V-U).
V = Speed of the train.
U = Speed of man.
Vr = (V-U).

If only one of the speed is given then how will we consider that which one is to be subtracted or not?

Why 5 - X not taken?

According to the question,

Trains length = 125m (distance).
Speed = 10sec,
Mans speed = 5km/hr.

The km the train hasn't travelled is not been given so take it as = X km/hr.
Man moves in the same direction = 5km/hr .

When two bodies are moving in the same direction then you will have to subtract it. If the person is moving on the opposite side he feels the train is moving faster hence u got to add But here it's on the same direction.

So, it's (x-5)km/hr.
When you want to convert kilometre into metres multiply with 5/18
So , (x-5) 5/18 ---> (1) i.e time

Time =distance/speed.
= 125/10 --> (2).

Therefore,
Time = distance/speed.
(X-5) 5/18 = 125/10,
(X-5)5/18 = 25/2,
(X-5) = 25/2 * 18/5 (simple cancellation).
(X-5) = 45,
X= 45+ 5,
X= 50.

D = S X T.

(125 + 0) = (X-25/18) X 10 --> (i)

{Whereas 125 = length of the train, 0 = length of man, X is taken as the speed of the train, 25/18 is 5X5/18 to convert m/s into km/h, "-" Minus is used because they are running in the same direction, 10 is time to cross man}

Now solve the equation (i) and we will get the answer.

125m
5km/hr
10sec
Speed=distance/time.

Therefore S=km/hr(it's convert to m/sec)
S=1000m/3600sec
S=5/18.

Therefore S=D/T
D=125m
T=10sec
S=125/10
S=12.5, S=5/18.

Therefore 12.5=5/18=S(cross multiplication)
S = 12.5 * 18/5.
S = 225/5,
S = 45km/hr.

Remaining train running speed is added.
Therefore S = 45 + 5.
= 50km/hr.

They should mention "relative speed" in the question. Why it is not so? It confuses the examiner!

How we say 45 km/hr is a relative speed?

Man's speed=5 km/hr = 5 * 5/18 = (25/18)m/s.
The distance covered by man in 10 sec = (25/18)*10=(250/18)m,
Therefore distance covered by train for crossing the man=125+250/18=1250/9m,
Therefore speed=(1250/9)/10=125/9 m/s,
=(125/9)*3600/1000,
=(125/9)*(18/5)=50 km/hr.

Why ((a+b)/(u-v)) = t does not work?

Where a=length of the train (125 meters).
b= length of object( 0 meter),
u = speed of train ( let, x m/s),
t = time taken to cross the object,
v = speed of object (5 km/hr).