(41) A train of length 360 meters is running at a speed of 48 km/hr. How long does it take to cross a 120-meter-long bridge?
Answer : 36 seconds
Explanation
To calculate the time it takes for the train to cross the bridge, we need to find the total distance the train needs to travel, which is the sum of the train’s length and the bridge’s length:
Total distance = Train length + Bridge length = 360 meters + 120 meters = 480 meters
Next, we need to convert the train’s speed from km/hr to m/s:
Speed = 48 km/hr * (1000 m/km) / (3600 s/hr) = 48000 m/hr / 3600 s/hr = 13.33 m/s (approximately)
Now, we can calculate the time it takes for the train to cross the bridge by dividing the total distance by the train’s speed:
Time = Total distance / Speed = 480 meters / 13.33 m/s ≈ 36.03 seconds
Therefore, it takes approximately 36 seconds (rounded to the nearest whole number) for the train to cross the 120-meter-long bridge.
(42) A train of length 250 meters is running at a speed of 20 km/hr. How long does it take to cross a 30-meter-long tunnel?
Answer : 50.39
Explanation
To calculate the time it takes for the train to cross the bridge, we need to find the total distance the train needs to travel, which is the sum of the train’s length and the bridge’s length:
Total distance = Train length + Bridge length = 250 meters + 30 meters = 280 meters
Next, we need to convert the train’s speed from km/hr to m/s:
Speed = 20 km/hr * (1000 m/km) / (3600 s/hr) = 20000 m/hr / 3600 s/hr ≈ 5.56 m/s (approximately)
Now, we can calculate the time it takes for the train to cross the bridge by dividing the total distance by the train’s speed:
Time = Total distance / Speed = 280 meters / 5.56 m/s ≈ 50.36 seconds
Therefore, it takes approximately 50 seconds (rounded to the nearest whole number) for the train to cross the 30-meter-long bridge.
The total distance the train needs to travel is 250 + 30 = 280 meters.
The speed of the train is 20 km/hr, which is equal to 5.556 m/s.
The time it takes the train to cross the tunnel is 280 / 5.556 = 50.39 seconds.
So the answer is 50.39
(43) A train of length 650 meters is running at a speed of 52 km/hr. In how many seconds will it pass a tree standing near the railway track?
Answer : 45 seconds
Explanation
To calculate the time it takes for the train to pass a tree, we need to find the distance the train needs to travel, which is equal to its length:
Distance = Train length = 650 meters
Next, we need to convert the train’s speed from km/hr to m/s:
Speed = 52 km/hr * (1000 m/km) / (3600 s/hr) = 52000 m/hr / 3600 s/hr ≈ 14.44 m/s (approximately)
Now, we can calculate the time it takes for the train to pass the tree by dividing the distance by the train’s speed:
Time = Distance / Speed = 650 meters / 14.44 m/s ≈ 45.01 seconds
Therefore, it takes approximately 45 seconds (rounded to the nearest whole number) for the train to pass the tree standing near the railway track.
(44) Two trains are running on parallel lines in the same direction at 15 km/hr and 35 km/hr. The faster train takes 5 minutes to pass the slower train. What is the length of the slower train?
Answer : 1250 meters
Explanation
Let the length of the faster train be L1 and the length of the slower train be L2. Since the trains are running in the same direction, we need to find their relative speed. The relative speed is the difference between their speeds, which is 35 km/hr – 15 km/hr = 20 km/hr.
Now, we need to convert the relative speed from km/hr to meters per second by multiplying by (1000 m/km) and dividing by (3600 s/hr):
Relative speed = (20 km/hr) * (1000 m/km) / (3600 s/hr) = 20000 m/hr / 3600 s/hr = 5.56 m/s (approximately)
The faster train takes 5 minutes (300 seconds) to pass the slower train, so in that time, the faster train covers the combined length of both trains (L1 + L2) at the relative speed:
Distance = Relative speed * Time L1 + L2 = 5.56 m/s * 300 s = 1668 m
We need to find the length of the slower train (L2). To do this, we need to calculate the distance the slower train travels during the 300 seconds:
Distance = Speed * Time L2_distance = (15 km/hr) * (1000 m/km) / (3600 s/hr) * 300 s = 1250 m
Now we can find the length of the faster train (L1) by subtracting the distance traveled by the slower train (L2_distance) from the combined length (L1 + L2):
L1 = L1 + L2 – L2_distance L1 = 1668 m – 1250 m = 418 m
Now we can use the length of the faster train to find the length of the slower train. Since the faster train takes 5 minutes to pass the slower train and covers both trains’ lengths, we know that during this time, the faster train travels a distance equal to the length of the slower train (L2) plus its own length (L1):
L1 + L2 = 418 m + L2 = 1668 m
Subtracting 418 m from both sides gives us the length of the slower train:
L2 = 1668 m – 418 m = 1250 m
So, the length of the slower train is 1250 meters.
(45) A train of length 430 meters is running at a speed of 36 km/hr. How long does it take to cross a 170-meter-long platform?
Answer : 60 seconds
Explanation
Convert the speed of the train from km/hr to m/s.
36 km/hr = 36000 m / 3600 s = 10 m/s
Find the total distance that the train needs to travel.
The total distance is equal to the length of the train plus the length of the platform.
430 m + 170 m = 600 m
Divide the total distance by the speed of the train to find the time it takes the train to cross the platform.
600 m / 10 m/s = 60 s
Therefore, it takes the train 60 seconds to cross the platform.
