(16) A train of length 370 meters is running at a speed of 66 km/hr. How long does it take to cross a 230-meter-long platform?
Answer : 32.73 seconds
Explanation
To cross the platform, the train will need to cover a distance equal to its own length plus the length of the platform. Therefore, the total distance to be covered by the train is:
Total distance = length of train + length of platform = 370 + 230 = 600 meters
We know that the speed of the train is 66 km/hr. To calculate the time taken by the train to cross the platform, we need to convert the speed from km/hr to m/s.
Speed of train = 66 km/hr = 66 x (5/18) m/s = 55/3 m/s
Now, we can use the formula:
time = distance / speed
To find the time taken by the train to cross the platform.
time = 600 / (55/3) = 32.73 seconds (approx)
Therefore, it will take approximately 32.73 seconds for the train to cross a 230-meter-long platform.
(17) Two trains of lengths 450 meters and 550 meters are running on parallel lines in the opposite direction at 60 km/hr and 70 km/hr. In how many seconds will the trains pass each other?
Answer : 27.69 seconds
Explanation
When two trains are running on parallel lines in opposite directions, the relative speed between them is the sum of their speeds. Therefore, the relative speed between the two trains is:
Relative speed = (60 + 70) km/hr = 130 km/hr = 130 x (5/18) m/s = 325/9 m/s
To find the time taken by the trains to pass each other, we need to calculate the distance covered by them in that time. When the two trains are passing each other, the distance covered by them is equal to the sum of their lengths. Therefore, the total distance covered by the two trains is:
Total distance = length of first train + length of second train = 450 + 550 = 1000 meters
Now, we can use the formula:
time = distance / speed
To find the time taken by the two trains to pass each other.
time = 1000 / (325/9) = 27.69 seconds (approx)
Therefore, the two trains will pass each other in approximately 27.69 seconds.
(18) Two trains of equal length are running on parallel lines in the opposite direction at 65 km/hr and 75 km/hr. The trains pass each other in 25 seconds. The length of each train is?
Answer : 500 meters
Explanation
Let the length of each train be x meters.
The relative speed of the trains is 65 km/hr + 75 km/hr = 140 km/hr.
140 km/hr = 140,000 m / 3,600 s = 40 m/s.
The total distance the trains need to travel is 2x meters.
The time it takes the trains to pass each other is 25 seconds.
Therefore, we have the equation:
2x / 25 = 40
x = 40 * 25 / 2 = 500 meters.
Therefore, the length of each train is 500 meters.
(19) A train of length 520 meters is running at a speed of 80 km/hr. How long does it take to cross a 280-meter-long station?
Answer : 36 seconds
Explanation
To cross the station, the train will need to cover a distance equal to its own length plus the length of the station. Therefore, the total distance to be covered by the train is:
Total distance = length of train + length of station = 520 + 280 = 800 meters
We know that the speed of the train is 80 km/hr. To calculate the time taken by the train to cross the station, we need to convert the speed from km/hr to m/s.
Speed of train = 80 km/hr = 80 x (5/18) m/s = 200/9 m/s
Now, we can use the formula:
time = distance / speed
To find the time taken by the train to cross the station.
time = 800 / (200/9) = 36 seconds (approx)
Therefore, it will take approximately 36 seconds for the train to cross a 280-meter-long station.
(20) Two trains are running on parallel lines in the same direction at 35 km/hr and 55 km/hr. The faster train takes 120 seconds to pass the slower train. What is the length of the faster train?
Answer : 662.4 meters
Explanation
The faster train is traveling at a speed of 55 km/hr, which is equal to 55000 m / 3600 s = 15.24 m/s.
The slower train is traveling at a speed of 35 km/hr, which is equal to 35000 m / 3600 s = 9.72 m/s.
The relative speed of the trains is 15.24 m/s – 9.72 m/s = 5.52 m/s.
The time it takes the faster train to pass the slower train is 120 seconds.
The length of the faster train is 5.52 m/s * 120 seconds = 662.4 meters.
So the answer is 662.4
