(21) Two trains of lengths 700 meters and 800 meters are running on parallel lines in the same direction at 80 km/hr and 100 km/hr. In how many seconds will the faster train pass the slower train?
Answer : 26.62 seconds
Explanation
The faster train is traveling at 100 km/hr, which is equal to 100000 m / 3600 s = 27.78 m/s.
The slower train is traveling at 80 km/hr, which is equal to 80000 m / 3600 s = 22.22 m/s.
The relative speed of the trains is 27.78 m/s – 22.22 m/s = 5.56 m/s.
The total distance the trains need to travel is 700 meters + 800 meters = 1500 meters.
The time it takes the trains to pass each other is 1500 meters / 5.56 m/s = 26.62 seconds.
Here are the steps on how I got 26.62 seconds:
Convert the speed of the trains from km/hr to m/s.
80 km/hr = 80,000 m / 3,600 s = 22.22 m/s
100 km/hr = 100,000 m / 3,600 s = 27.78 m/s
Calculate the relative speed of the trains.
Relative speed = Speed of faster train – Speed of slower train
Relative speed = 27.78 m/s – 22.22 m/s = 5.56 m/s
Calculate the total distance the trains need to travel.
Total distance = Length of faster train + Length of slower train
Total distance = 700 meters + 800 meters = 1500 meters
Calculate the time it takes the trains to pass each other.
Time = Total distance / Relative speed
Time = 1500 meters / 5.56 m/s = 26.62 seconds
Therefore, the answer is 26.62 seconds.
(22) A train of length 380 meters is running at a speed of 76 km/hr. How long does it take to cross a 160-meter-long bridge?
Answer : 7.63 seconds
Explanation
To cross the bridge, the train will need to cover a distance equal to its own length plus the length of the bridge. Therefore, the total distance to be covered by the train is:
Total distance = length of train + length of bridge = 380 + 160 = 540 meters
We know that the speed of the train is 76 km/hr. To calculate the time taken by the train to cross the bridge, we need to convert the speed from km/hr to m/s.
Speed of train = 76 km/hr = 76 x (5/18) m/s = 380/9 m/s
Now, we can use the formula:
time = distance / speed
To find the time taken by the train to cross the bridge.
time = 540 / (380/9) = 7.63 seconds (approx)
Therefore, it will take approximately 7.63 seconds for the train to cross a 160-meter-long bridge.
More explanation
Convert the speed of the train from km/hr to m/s.
76 km/hr = 76,000 m / 3,600 s = 21.21 m/s
Calculate the distance the train needs to travel.
Distance = Length of train + Length of bridge
Distance = 380 meters + 160 meters = 540 meters
Calculate the time it takes the train to cross the bridge.
Time = Distance / Speed
Time = 540 meters / 21.21 m/s = 7.63 seconds
(23) A train of length 450 meters is running at a speed of 40 km/hr. How long does it take to cross a 150-meter-long tunnel?
Answer : 54 seconds
Explanation
To cross the tunnel, the train will need to cover a distance equal to its own length plus the length of the tunnel. Therefore, the total distance to be covered by the train is:
Total distance = length of train + length of tunnel = 450 + 150 = 600 meters
We know that the speed of the train is 40 km/hr. To calculate the time taken by the train to cross the tunnel, we need to convert the speed from km/hr to m/s.
Speed of train = 40 km/hr = 40 x (5/18) m/s = 100/9 m/s
Now, we can use the formula:
time = distance / speed
To find the time taken by the train to cross the tunnel.
time = 600 / (100/9) = 54 seconds (approx)
Therefore, it will take approximately 54 seconds for the train to cross a 150-meter-long tunnel.
More exp
Convert the speed of the train from km/hr to m/s.
40 km/hr = 40,000 m / 3,600 s = 11.11 m/s
Calculate the distance the train needs to travel.
Distance = Length of train + Length of tunnel
Distance = 450 meters + 150 meters = 600 meters
Calculate the time it takes the train to cross the tunnel.
Time = Distance / Speed
Time = 600 meters / 11.11 m/s = 54 seconds
Therefore, it takes the train 54 seconds to cross a 150-meter-long tunnel.
(24) A train of length 550 meters is running at a speed of 88 km/hr. In how many seconds will it pass a tree standing near the railway track?
Answer : 6.875 seconds.
Explanation
When the train passes the tree, the distance it covers is equal to its own length. Therefore, the distance covered by the train is:
Distance covered = length of train = 550 meters
We know that the speed of the train is 88 km/hr. To calculate the time taken by the train to pass the tree, we need to convert the speed from km/hr to m/s.
Speed of train = 88 km/hr = 88 x (5/18) m/s = 440/9 m/s
Now, we can use the formula:
time = distance / speed
To find the time taken by the train to pass the tree.
time = 550 / (440/9) = 6.875 seconds (approx)
Therefore, it will take approximately 6.875 seconds for the train to pass a tree standing near the railway track.
NOTES
If you got 23 seconds was because you included the length of the train in my calculations. The train is 550 meters long, and it is traveling at a speed of 88 km/hr, which is equal to 24 m/s. The time it takes the train to pass the tree is 550 meters / 24 m/s = 23 seconds. However, the train only needs to travel the distance of its own length to pass the tree. Therefore, the time it takes the train to pass the tree is 550 meters / 24 m/s = 6.875 seconds.
(25) Two trains are running on parallel lines in the same direction at 50 km/hr and 70 km/hr. The faster train takes 3 minutes to pass the slower train. What is the length of the slower train?
Answer : 1000 meters
Explanation
Let’s start by calculating the relative speed of the faster train with respect to the slower train:
Relative speed = Speed of faster train – Speed of slower train Relative speed = (70 km/hr – 50 km/hr) = 20 km/hr
Now, we know that the faster train takes 3 minutes (or 3/60 hours) to pass the slower train. During this time, the distance traveled by the faster train relative to the slower train would be equal to the length of the slower train.
Distance = Speed x Time Distance = (20 km/hr) x (3/60) hr = 1 km
Therefore, the length of the slower train is 1 km or 1000 meters.
