Aptitude - Problems on Trains - Discussion

Hey guys, don't much obsessed with it. It's quite simple as it is.

1 mile=1.609 km.

Distance travelled by train = (7/2+1/4) only.

For easy understanding.

Assume that you are standing at the tunnel starting end with a stopwatch and now the train is coming and (note that in the question he said that from the front end entres) that means when the engine comes to the position where you are standing then you start the stopwatch from that point, the train goes on goes on and after some time the engine part reaches to the exit end of the tunnel and (note that in the question he said time should be calculated till the rear emerges) so don't stop the stopwatch let the train go and the strain is going going going and after some time the last bhogi (last part) of the train left the tunnel then you need to stop the stopwatch.

Then note the time. So that time is only required.

Observe carefully in this entire process the train is travelling only the tunnel length and its own length.

And coming to question.

The question is error instead of metres he has given miles.

So don't bother much about this.

If you guys have any doubt about the above explanation just take a pen and paper and draw a line and observe the above explanation. Then You guys get that.

I hope you understand.

Have a nice day.

Ya friends let me explain it in detail, hope this will help you,

Given the speed of train = 75 mph which means (miles per hr). Because logically speaking there will be no train moving only 75 meters per one hour.

Tunnel length = 3 1/2.
= (3*2+1)/2 = 7/2 miles.
Train length = 1/4 mile.

So now as every thing is given in miles there is no need of any conversion. Now let us go to the problem.

For a train of length 'l' to cross a stationary object of length 'b' the time taken is equal to the time taken to cover (l+b) miles;

= 7/2+1/4.
Taking lcm as 4.
= ( (7*2) +1) /4.
=15/4.

Now the main confusion is to add another 1/4 distance or not. Here is the solution. It is not needed because.

At the start of train we are considering at entrance of the tunnel, so train length is not to be considered at starting end. But at the rear end of the tunnel it was said that trains rare end is to be passed, so rain length is to be added only once.

Now Speed = Distance/Time,
So, Time = Distance/Speed,

Now from above calculation.
Distance = 15/4 miles,
Speed = 75 miles per hour = 15/4 miles.

Time=-----------------75 miles/hr.

T = (15/ (75*4) ) hr.
T = 1/20 hrs.
T = 1/20*60 mins.
T = 3 minutes.

So the answer is 3 minutes.

We have given 3(1/2) mile length of the tunnel and train length as 1/4 mile.
So we relate tunnel length and train length

We have to see in 3 1/2 how many 1/4's are there or how many 1/4's make a 3 1/2
3 1/2 is a mixed fraction to make into a proper fration we do as follows
first multiply 2*3=6
next add the numerator 1 to previous results
6+1=7

We have numerator as '7'and keep the denominator '2' as it is
now the proper fraction for 3 1/2 is 7/2

So here total length 7/2+1/4=15/4miles
time taken=distance/speed
time taken=(15/4miles)/75miles/hr
15/4*75=15/300=>1/20hrs
to convert into min v multiply by 60 .
because 1 hr = 60 min
1/20 *60=3mins
here ends the problem

No need of convert miles to kms because it makes the problem complex and even though all units are in miles they get cancelled.

Answer is 3 min because.

Given is speed = 75 miles per hour
Total distance is 7/2 + 1/4 = 15/4

Distance is 15/4 because in question it is mentioned that calculate time from entry of tunnel to the point when train's rear left the tunnel.

                        7/2 miles              1/4 miles
           <---------------------------------><------->
            _________________________________   train
 entry of  [               tunnel            ]__________
  tunnel   [_________________________________]__________]--> -->

Hope so this will help.

Guys 1mile = 1.6km.
For train speed:
So 75mph = 75*1.6 = 120kmph.

For tunnel length and train length:
7/2miles*1.6=5.6km and 1/4miles*1.6=0.4km.
So total distance=5.6+0.4=6km.

Now to calculate the time we have the formulae is t=d/s.
Lets convert all data into metres.
So 6km*1000=6000m.

Speed=120*5/18 m/sec=100/3 m/sec.
So t=6000/100/3 which is equal to 18000/100=180seconds.

So to convert seconds into minutes is(1min=60sec) 180/60=3min.
Try to understand because it's too long.

Answer is 3.2, because Train length=1/4 mile,Tunnel=3.5 i.e 7/2 mile, When train enter in to the tunnel Time need to start till last rear end come out from the tunnel.
that's why 7/2+1/4+1/4=16/4= 4 miles.

Time stop[ end 7/2 tnl start ](Time start)
1/4 Srt<-------End
Start<---------End.
this above figure shows "3 min",but we need to count till rare end of train.
I hope u understand.

@vinit: Nope! Look, we need to calculate time taken by the train to cover the "inside" of the tunnel :
1)When "Front emerges".. no part of the train is 'inside' the tunnel.. therefore distance covered till nw = 0
2) when the front emerges out.. it has covered the whole distance of the tunnel = 7/2
3) rest of the train is still inside the tunnel (as only the front has emerged out).. so now the remaining train comes out.. Hence 7/2 + 1/4

Here, consider only the head of the train. If the train is entering the tunnel, the head is at the entrance of the tunnel (obviously). After the train's head is reached at the end of the tunnel, it has covered a distance of the length of the tunnel. But we want the tail of the train to be at the end of the tunnel.

So, the train will have to move the distance equal to it's length. Now, it's clear that total distance=tunnel length+train length.

Let me try to make this clear in 2 points.

#1. This question is same as train crossing the platform
#2. If we keep on reducing the size of tunnel till it reaches to size zero,i.e., the tunnel has now become a point so now we will calculate the time by using the length of the train only once. now when the size of the tunnel is added we can calculate time by Length of the train + Length of the tunnel / speed of the train.

Time=Distance/velocity ---------------------(1)
time=(15/75*4)=1/20 hrs ---------------------(2)
time=(1/20)*60=3 min ---------------------(3)

I understand all these statement, but i have problem. with the statement (2) that how we just find out the time without converting meter into miles or vice versa. In this they simply find the time without any conversion and it is not so acceptable

Please clear me out..