Aptitude - Problems on Trains - Discussion

Here given two trains moving in opposite directions;

Formula:
Time = (L₁ + L₂) / (S₁ + S₂)

Given:
L₁ = 270 m
L₂ = ?

S₁ = 120 × 5/18 = 100/3 m/s.
S₂ = 80 × 5/18 = 200/9 m/s.

Substitute:

9 = (270 + L₂) / (100/3 + 200/9)
9 = (270 + L₂) / (500/9),
270 + L₂ = 9 × (500/9),
270 + L₂ = 500,
L₂ = 500 − 270,
L₂ = 230 m.

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.

Thanks everyone, for explaining it.

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.

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.

L1 = 270, L2 =?.

T = D/S
S = 120+80Km/h, S = 200*5/28, S= 500/9,
T = 9 Second,
270 + L2/500/9 = 9,
L2 = 500 - 270,
2 = 230.

Length of 2nd train = 230 M.

Here x + 270/9 = 500/9.

How to simplify this? Please explain.

Step-1:

Distance = 250m,
Speed = 72*5/18 = 20,
Time = 26 sec.

Step-2:
Formula d=s*t,
250m=20*26,
250m = 520,
M= 520- 250.
m =270 ans.

how we take x+270÷9? Please explain.

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?