Aptitude - Problems on Trains - Discussion

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.

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.

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.

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.

Here x + 270/9 = 500/9.

How to simplify this? 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?

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.

On cross multiplication we get,

9 (500) =4500.
Then, 9 (270+x), 9 goes to another side.
270+x=4500/9,
270+x=500,
X=500-270.

Finally, we get 230.

Distance =speed *time,
D=120+80km/h*9,
D=200*5/18*9,
D=1000/2,
D=500-270=230m.

Opposite direction: Adding.
Same Direction: Subtract.