Aptitude - Problems on Trains - Discussion

L of train A= 100m.
L of train B= 100m.

Time taken for trains to cross each other= 8s.
Assume the speed of Train A= you.
Assume the speed of Train B= 2u since the rate of one train is twice the speed of the other.
Both trains are running in opposite directions hence, use the formula.
The Time is taken to cross each other= (L of train A + L of train B) / (speed of train A + speed of train B).

Substituting: 8sec= (100m+100m) / (u+2u) ;.
8sec= 200m/3u.
Cross multiply 8sec*3u=200m.
24uSec=200m; Divide both sides by 24Sec.
U= 25m/3Sec or 8. 33333m/sec.

Therefore, the speed of a faster train (i.e train with a speed twice as fast as the other) = 2u= (2*25) /3 or 2*8. 3333= 50/3 m/sec.

Convert the answer to km/hr by dividing the answer by 5/18.

= (50/3) / (5/18) = (50*18) / (3*5) = 60km/hr.

Let speed be x and 2x kmph.

The total relative speed of the two trains = 3xkmph.
3600secs = 3000x.
1sec = 3000x/3600,
8secs=3000x/3600×8,
= 20x/3.
Btp;
20x/3 = 200,
x = 200×3/20,
=30.

Speed of slower train = 30kmph.
The faster train = 30 × 2 = 60kmph.

Let the speed of the slower train be "x" m/s.

Since the faster train is moving twice as fast, its speed is "2x" m/s.
When two trains moving in opposite directions cross each other, their relative speed is the sum of their individual speeds.
So, the relative speed of the two trains is (x + 2x) m/s = 3x m/s.
Distance traveled by each train to cross each other is 100 meters (the sum of their lengths).
Now, we can use the formula: Distance = Speed × Time.

In this case, Distance = 100 meters and Time = 8 seconds.

So, 100 = 3x × 8.
Now, solve for x:
100 = 24x,
x = 100/24,
x = 25/6,
x = 4.1667 m/s (approximately).

So, the speed of the slower train is approximately 4.1667 m/s, and the speed of the faster train is twice that, which is 2 * 4.1667 ≈ 8.3333 m/s.
Therefore, the speed of the faster train is approximately 8.3333 m/s.
Converted to Km/hr is 30Km/hr.

Here it is said that Relative speed is x + 2x (in opp. Direction).
So if you solved this then you get 30 km/hr but there is a catch the question said "If one is moving twice as fast as the other, then the speed of the faster train is" Currently 30 km/hr are following both train but question said what if faster has 2 X current speed, then calculate the faster train is 2 X 30 km/hr = 60 km/hr.