Aptitude - Problems on Trains - Discussion

How did this equation x-5=45 form?

If the man and train in opposite direction then it relative speed is x+5. And speed is x+5=45. =>x=40. Am I right?

Any basic formula is there for this problem kindly explain.

Why we are multiplying the 18/5 ?
or we can ask that why we are divide ?

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?

If we convert km/hr into m/sec i.e. 1000/3600 it's come 5/18. So why it is calculation is 125/10*18/5 instead of 5/18?

It is given that
Speed of man=5km/hr
Distance travelled by man in 10s=125/9m
Distance travelled by train in 10s= {125+(125/9)}m
Hence
Speed of train = [{125+(125/9)/10]*3600 = 50 km/hr

Speed of train=(length of train/time) is a formula
hence,
125/10 m/sec
now (125/10)*(18/5)=45.. multiply by 18/5 to become km/h
now 45 is relative speed
sr=s1-s2
45=s1-5
s1=50

Why it is subtracted ? please explain.

A Train 125m long passes a man,running at 5km/hr.

It means that train speed =5000m/3600sec.------(1hr=60*60=3600sec & 1km=1000meters).

& Second Train running on same Direction & Passed in 10sec's.

It means Second train cross distance within 10sec's.

Speed of Train for meters/10sec = 5000m/3600sec*10sec=1.388888888889m
So,that train speed for km/hr=speed of train for 10 sec * remaining 3590 Seconds(3600-10).
=1.3888888889*3590=49.8611111111111111=50km/hr.

Therefore, A speed of that train=50km/hr.

This is simple. Length of the train is given and the seconds is given.

So we have m/sec there. To convert it to km/hr,

1km= 1000 m and 1 hr = 3600 sec.

So km/hr= 1000/3600. So we have 18/5. Now we got our km/hr.

Well that guy is running at 5 km speed. So we take the train speed as x and subtracting the 5 km speed from that. We have x-5 as the train speed. Now x-5= 45. So x= 45+5=50. :-).