Aptitude - Problems on Trains - Discussion

A train of length 110mtr travelling at a speed of 80km/hr. Find the time taken by that train to overtake a train having length 130mtr travelling at a speed of 62km/hr?

@Preethi.

Relative speed u-v = 80-62= 18km/hr=(18* 5/18)= 5 m/s.

Total length a+b = 110+130= 240 m.

Time to overtake = (a+b)/(u-v)[see formula 9 from formula section]

= 240/5

= 48 sec.

Am I correct?

How we come to know that the speed 5km\hr is the speed of the man because it is not given in the question?

@Diksha.

A train 125 m long passes a man, running at 5 km/hr in the same direction means the , in between man and running is for confusing you it should be taken as 125 m long train passes a man running at 5 km/hr.

Why we are using 18/5 instead of 5/8 is as follows,
1km = 1000m.
1hr = 3600s.

So 1km/hr = (1000/3600)m/s.
Hence 1km/hr = (5/8)m/s.

Then 5/8 becomes reverse as 8/5 and it will becomes as,

(8/5)km/hr = m/s.

Again you get a doubt that why it converts into m/s because check our problem has 125 m and also they gave 10 seconds.

So (125/10)m/s.

Here the train is crossing a moving object rather than a stationary object like a pole. Then how it is possible to say its relative speed to man is (125/10) m/sec ?

This solution easy to understand:

Convert man speed from km/hr into meter/sec.

5km/hr = 5*1000m/3600sec or 25m/18sec.

Since 18sec = 25meter.

10sec = ? meter.

So it would be 25*10/18 = 125/9 meter.

So man complete 125/9 meter in 10 sec.

Train complete distance in 10 sec = 125 meter (train length) + 125/9 meter of man.

So it would be 10 = 125+125/9 or 10 sec = (1125+125) /9 meter or 10*9 sec=1125+125 meter or 90 sec = 1250 meter or 125 meter/9sec or convert it into km/hr so it be 125m/9s * 18/5 = 50 km/hr.

So train speed is 50 km/hr.

To convert km/hr into m/s it is multiplied by 5/18 or 1000/3600.

And from m/s into km/hr multiplied by 18/5 k done.

Can anyone explain how to find length of train when the train speed and person speed given?

60min -> 5km.

1min->? =>(1*5)/60 = 1/12km.

For 1 second -> (1/12)/60 = 1/720km.

For 10 second ->(1/720)*10 = 1/72km.

It means train covered 1/72km in 10second, then calculate how much distance that train can cover in 60 min(1 hour). Because they've given the choices in km/hr.

=>(1/72)*(60*60)=50km/hr.

Note: Length of the train is not required in the calculation.

Distance covered by man = 5*5/18*10.

= 250/18 Meter.

Total Distance covered by Train = 125+250/18 = 2500/18 Meter.

So Train speed = (2500/18)/10 Meter/Second.

or = 2500/180*18/5 Km/Hr.

= 50 Km/Hr.