(6) A train of length 450 meters is running at a speed of 54 km/hr. In how many seconds will it pass a man standing near the railway track?
Answer : 30 seconds
Explanation
To pass the man standing near the railway track, the train will need to cover a distance equal to its length plus the distance between the man and the train when the train starts passing him.
Let’s assume that the distance between the man and the train when the train starts passing him is x meters.
Therefore, the total distance to be covered by the train to pass the man is:
Total distance = length of train + distance between man and train = 450 + x meters
We know that the speed of the train is 54 km/hr. To calculate the time taken by the train to pass the man, we need to convert the speed from km/hr to m/s.
Speed of train = 54 km/hr = 54 x (5/18) m/s = 15 m/s
Now, we can use the formula:
time = distance / speed
To find the time taken by the train to pass the man.
time = (450 + x) / 15
We can see that the distance covered by the train and the distance between the man and the train are directly proportional to each other. This means that if the distance between the man and the train is halved, the time taken by the train to pass the man will also be halved.
Therefore, we can assume that the distance between the man and the train is zero. In other words, the man is standing right at the edge of the railway track.
When the train passes the man, the distance covered by the train will be equal to its length. Therefore, we can set the total distance to be covered by the train to 450 meters.
time = 450 / 15 = 30 seconds
Therefore, it will take 30 seconds for the train to pass a man standing near the railway track.
(7) Two trains are running on parallel lines in the same direction at 40 km/hr and 60 km/hr. The faster train takes 1 minute to pass the slower train. What is the length of the faster train?
Answer : 200 meters
Explanation
When the faster train is passing the slower train, the distance it covers is equal to the sum of the lengths of the two trains. Let’s assume that the length of the slower train is L1 meters and the length of the faster train is L2 meters.
We know that the two trains are running in the same direction and the faster train is overtaking the slower train. Therefore, the relative speed between the two trains will be the difference between their speeds.
Relative speed = (60 – 40) km/hr = 20 km/hr = 20 x (5/18) m/s = 50/9 m/s
We also know that the faster train takes 1 minute to pass the slower train. Therefore, we can write:
(L1 + L2) / (50/9) = 60 seconds
Simplifying this equation, we get:
L1 + L2 = (50/9) x 60
L1 + L2 = 500 meters
We know that the length of the slower train is 300 meters. Therefore, we can substitute the value of L1 in the above equation to get:
300 + L2 = 500
L2 = 200 meters
Therefore, the length of the faster train is 200 meters.
(8) A train of length 350 meters is running at a speed of 45 km/hr. How long does it take to cross a 250-meter-long platform?
Answer : 48 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 = 350 + 250 = 600 meters
We know that the speed of the train is 45 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 = 45 km/hr = 45 x (5/18) m/s = 25/2 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 / (25/2) = 48 seconds
Therefore, it will take 48 seconds for the train to cross a 250-meter-long platform.
(9) A train of length 480 meters is running at a speed of 64 km/hr. How long does it take to cross a 320-meter-long station?
Answer : 45 seconds
Explanation
To determine the time it takes for the train to cross the 320-meter-long station, we first need to find the total distance the train travels while crossing the station.
The total distance is the sum of the length of the train and the length of the station:
Total distance = Length of train + Length of station Total distance = 480 meters + 320 meters Total distance = 800 meters
Next, we need to convert the train’s speed from km/hr to meters per second (m/s) using the conversion factor:
1 km/hr = 1000/3600 m/s
So, the train’s speed in m/s is:
64 km/hr × (1000/3600) m/s = 64 × (10/36) m/s ≈ 17.78 m/s (approximately)
Now we can use the formula:
Time = Distance / Speed
Time = 800 meters / 17.78 m/s ≈ 45 seconds (approximately)
It will take approximately 45 seconds for the train to cross the 320-meter-long station.
(10) Two trains are running on parallel lines in the same direction at 75 km/hr and 55 km/hr. The faster train takes 90 seconds to pass the slower train. What is the length of the slower train?
Answer : 500.4 meters
Explanation
Let’s denote the length of the slower train as L (in meters). Since the trains are moving in the same direction, their relative speed is the difference between their individual speeds, which is 75 – 55 = 20 km/hr.
To convert the relative speed from km/hr to meters per second (m/s), we can use the following conversion factor:
1 km/hr = 1000/3600 m/s
Therefore, the relative speed of the two trains in m/s is:
20 km/hr × (1000/3600) m/s = 20 × (10/36) m/s = 5.56 m/s (approximately)
Now, we know that the faster train takes 90 seconds to pass the slower train. We can use the formula:
Distance = Speed × Time
Since the faster train is passing the slower train, the distance traveled by the faster train while passing the slower train is equal to the length of the slower train (L).
So, L = 5.56 m/s × 90 s
Solving for L:
L = 500.4 m
Thus, the length of the slower train is approximately 500.4 meters.
