Aptitude - Problems on Trains - Discussion

The first train is 270 meters long.
It runs at a speed of 120 km/h.
The second train runs in the opposite direction at 80 km/h.
Both trains cross each other in 9 seconds.
We need to find the length of the second train.
Now we need convert speeds into meters per second:

First train speed:
120*18/5 = (120*5)/18 = 600/18 = 33.33m/s.

Second train speed:
80*5/18 = (80*5)/18 = 400/18 = 22.22m/s.

Now, Find the total speed when the two trains run opposite.
When two trains run opposite each other, their speeds add up.
Total speed = 33.33+22.22,
= 55.55m/s.

Total distance= Total speed×Time.
= 55.55×9.
= 500meters.

Now,Find the length of the second train
Length of first train+Length of second train = 500
We know the first train length = 270 meters,
So,270+Length of second train = 500

Length of second train = 500 − 270 = 230.

What we know is:

t1 length=270m.
t1 speed = 120km/h or 33.33m/s.
t2 length = x,
t2 speed = 80km/h or 22.22m/s.
total speed = 9 seconds.

We need to find the relative speed, so its done like this because the trains are moving towards each other.

33.33m/s+22.22m/s = 55.55m/s.

Now we have all the information we need to solve the length of train 2.

270m+Xm
-------------- = 9s.
55.55m/s

Now we find the total length of both trains combined. We use the information we have. 55.55m/s is now converted to its opposite function, from division to multiplication. 55.55m/s * 9s = 499.95m.

So 499.95m is the total length of both trains combined, so now we can solve train 2's length by completing this final equation.

x= 499.95m-270m = 229.95m. round up to 230m, therefore train 2's length is 230m.

@Janani.

The concept of relative speed is still the basic time, speed and distance formula applied to distance between two moving bodies.

In a simple case of the distance.

Formula, a body traveling with a speed of 50 km/h is reducing the gap between its starting point and the finish point by 50 km every hour.
&
In the relative speed case of the distance formula two moving bodies, traveling at a relative speed of 50 km/h towards/away from each other, are reducing/increasing the gap between them by 50 km every hour.

Hope this help.

If the two trains cross opposite directions both are cross each other. So we need calculate crossing speed of the two trains. So we must add two trains speeds respectively. We assumed train A cross train B in a particular amount of speed as same as Train B also cross Train A.

Here two respective speeds are happen then only the process completed in a particular Time. Or we assume Train A is stable that time train B only cross Train A that is Train A speed is zero this is the logic I hope now you can understand.

In 9 seconds, First train crosses another train.

T = D/S.

Let, X be the length of the other train
Since, they are in opposite directions speeds should be added.

In train, since the distance travelled will be the length of each train we add them.
9sec = (270 + X )m / (120 + 80 ) km/hr.
9 * 200 * 5/18 m/sec = 270 + X ,
1800 * 5/18 = 270 + X,
100 * 5 = 270 + X,
500 = 270 + X.
230 = X.

If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then:

The time taken by the trains to cross each other =(a+b)/(u+v)

Then time is 9 sec, a=270 metres, b=x metres, u=120 kmph,
v=80 kmph

Therefore 9=(270+x)/(120+80)*5/18
we multiply (120+80) by 5/18 because converting kmph into m/sec
5/18*200*9=270+x
x=230

Find the distance covered by the Train 1 in the relative speed and the time given i.e 9 seconds, relative speed as calculated 500/9
distance = speed * time.

500/9*9 = 500 meters.

So, now by deducting the length of train 1 i.e 270 from 500;
500-270 = 230 the length of train 2.

Hi,

Can we do like this?

200 * 5/18 = 55.6

In above step is it correct or not, because after all post are look like step following.

200*5/18= 500/9 m/s .

Why not 200 * 5/18 = 55.6.

From above my step will be;
55.6 = (270+x)/6.
(270 + x) = 55.6 * 6 = 333.33.
x = 333.33 - 270 = 63.3 m.

Why not?

Use the formula, t = a+b/u+v, (train running opposite direction).

Where t = First train passes other train in time.

a+b = Length of train.

u = Speed of first train and v=speed of second train.

Then, 9 = 270+b/(120+80) km/hr.

<=> 270+b = 200 km/hr*9s = 500 m.

Now, b = 500-270 = 230 m.

Train Length=270m.
Speed=120km/h=120*(5/18)=32.4m/s.

Time= 9.

Train2 Length= X.
Speed of Train2=80km/h=80*(5/18)=21.6.

Relative Speed=32.4+21.6=54.00.
Relative Length=270 + X.

Speed=Distance/Time.
54=(270+X)/9.

(54*9)-270=X.

X=216.

Then How come 230?