Aptitude - Problems on Trains - Discussion

How to calculate what Km/Hr is train running if its length is 130 m and cross it own start point in 15 seconds?

Speed of the train relative to man = 125/10.

How they wrote it?

Moving in same direction : SUBTRACT.

Moving in opposite direction : ADD.

Can anyone please explain me why it is divided by 18/5 in place of 5/18?

Reason is 1 km/hr = 1000 m/3600 sec = 10/36 = 5/18.

So why it is used 18/5 in place of 5/18?

Please help me understand?

Distance travel by man in 10s = (5*1000*10)/(3600) = 13.89 m.

Now this much more distance the train has to travel due to mobile reference which is man.

Total distance travel by train = (125+13.89)m = 138.89 m.

Speed = (138.89*3600)/(10000) = 50 km/hr.

Comparison:

If I split the 138.89 into 125+13.89.

= 125/10+13.89/10 = 45+5 = 50 km/hr.

A different way to calculate this:

Length of the train: 125 m.

Distance traveled by man in 10 sec: 5*(5/18) m/s = 25/18 m for 1 sec.

i.e 4(25/18)*10 = 125/9 m for 10 sec.

Total distance traveled by train: 125 + 125/9 = 1250/9 m in ten seconds.

Speed for traveling 1250/9 m in 1 sec = (1250/9)/10 = 13.888.

In km = 13.888*(18/5) = 50 km/hr.

Relative speed of any two object say x km/h and why km/h moving in the same direction would always be (x-y) km/h.

Here the speed of the train is related to the man.

Hence relative speed = 125/10 m/s = 25/2 m/s.

The speed of the man is 5 km/h. When you convert it for m/s the speed will be (5x5/18) m/s = 25/18 m/s.

We know that relative speed,

R.S = (x-y) m/s or km/h.

Here x (unknown) , y= 25/18 m/s and R.S = 25/2 m/s.

Substituting we get,

X = (25/2)+(25/18).
X = 250/18 m/s (or) (250/18) x (18/5) km/h.

So X = 50 km/h.

Therefore the speed of the train will be 50 km/h. Hope you got it!.

Why is the distance covered by man in 10 sec not considered? I believe the total distance would be the length of train + distance covered by man in 10 sec. Considering this the relative speed of train comes out to 55 km/hr. Please suggest.

Let the speed of train= x km/hr.

So relativee speed = distance/time.

Relative speed of train = (x- 5) km/hr.

x-5 = 0.125/10/3600.

So x- 5 = 0.125x3600/10 = 45.

x = 45+5 = 50 km/hr answer.

In 10 sec man will cover 125/9 m. In the relative motion distance should be added in either cases (opposite direction or same direction). So relative speed should be (125+(125/9))/10. Please explain.