Aptitude - Problems on Trains - Discussion
Discussion Forum : Problems on Trains - General Questions (Q.No. 13)
13.
Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
Answer: Option
Explanation:
Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m/sec.
(100 + 100) | = 3x | |
8 |
24x = 200
x = | 25 | . |
3 |
So, speed of the faster train = | 50 | m/sec |
3 |
= | 50 | x | 18 | km/hr | |
3 | 5 |
= 60 km/hr.
Discussion:
73 comments Page 1 of 8.
Wanambwa Musa said:
7 months ago
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.
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.
(2)
Indraneel Mal said:
12 months ago
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.
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.
(4)
Cami said:
2 years ago
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.
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.
(1)
Aashu said:
2 years ago
@Fabarah Israr.
It's not 25/6 it's 25/3.
And it is asked to calculate the speed of a faster train.
x= 25/3 (speed of the slower train)
whereas the speed of the faster train is 2x, therefore 2*25/3 gives 50/3.
It's not 25/6 it's 25/3.
And it is asked to calculate the speed of a faster train.
x= 25/3 (speed of the slower train)
whereas the speed of the faster train is 2x, therefore 2*25/3 gives 50/3.
Fabarah Israr said:
2 years ago
Can someone please tell me, we are already multiplying 2 with x then why we are again multiplying with 2 with 25/6? Please explain me.
Innie said:
3 years ago
If x= 25/3, how is 2x= 50/3?
It should have been 50/6. Am I right?
It should have been 50/6. Am I right?
(1)
Nisha said:
3 years ago
How come 50/3? Please explain me.
Urid said:
3 years ago
Two train length is 100 m long each.
So, 100 + 100 = 200m.
Cross eachother in 9 sec so to find speed.
Speed = length/time.
Speed here ( one is moving twice as fast as the other).
If one train is x then another should be twice of x so 2x.
They are moving in opposite directions so x + 2x = 3x ( when moving in same direction we substract { u - v} in case of opposite direction { u+v}.
3x = 200m/9 sec * 18/5 (But the answer should be in km/s so we use 18/5).
3x = 90km/hr,
x = 90/3,
x = 60km/hr.
So, 100 + 100 = 200m.
Cross eachother in 9 sec so to find speed.
Speed = length/time.
Speed here ( one is moving twice as fast as the other).
If one train is x then another should be twice of x so 2x.
They are moving in opposite directions so x + 2x = 3x ( when moving in same direction we substract { u - v} in case of opposite direction { u+v}.
3x = 200m/9 sec * 18/5 (But the answer should be in km/s so we use 18/5).
3x = 90km/hr,
x = 90/3,
x = 60km/hr.
(3)
Roshan Kumar said:
3 years ago
Answer will be 30km/hr.
Because the simplification of 200/24 = 25/6.
But in the answer it's given as 25/3 that's why the answer is changed to 60 km/hr.
Because the simplification of 200/24 = 25/6.
But in the answer it's given as 25/3 that's why the answer is changed to 60 km/hr.
Riqual said:
4 years ago
@Nutan.
How come 18/3?
How come 18/3?
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