(31) Two trains of lengths 650 meters and 750 meters are running on parallel lines in the same direction at 60 km/hr and 80 km/hr. In how many seconds will the faster train pass the slower train?
Answer : 251.80 seconds
Explanation
First, we need to find the relative speed between the two trains. Since they are running in the same direction, we subtract the slower train’s speed from the faster train’s speed:
Relative speed = (80 km/hr) – (60 km/hr) = 20 km/hr
Now, we need to convert this relative speed from kilometers per hour to meters per second:
1 km = 1000 meters 1 hour = 3600 seconds
Relative speed = (20 km/hr) * (1000 meters/km) / (3600 seconds/hr) ≈ 5.56 m/s
Now, let’s find the total length of the trains, which is the distance the faster train needs to cover to pass the slower train:
Total length = 650 meters + 750 meters = 1400 meters
Finally, we can find the time it takes for the faster train to pass the slower train by dividing the total length by the relative speed:
Time = Distance / Speed Time = 1400 meters / 5.56 m/s ≈ 251.80 seconds
So, it will take approximately 251.80 seconds for the faster train to pass the slower train.
(32) A train of length 320 meters is running at a speed of 68 km/hr. How long does it take to cross a 140-meter-long bridge?
Answer : 24.35
Explanation
To solve this problem, we first need to determine the total distance that the train has to travel to completely cross the bridge. This distance includes the length of the train and the length of the bridge.
Total distance = Length of train + Length of bridge Total distance = 320 meters + 140 meters Total distance = 460 meters
Next, we need to convert the train’s speed from kilometers per hour (km/hr) to meters per second (m/s) since we’re dealing with meters.
1 kilometer = 1000 meters 1 hour = 3600 seconds
So, to convert 68 km/hr to m/s:
68 km/hr * (1000 m/km) / (3600 s/hr) = 18.89 m/s (approximately)
Now, we can use the formula:
Time = Distance / Speed
Time to cross the bridge = Total distance / Train’s speed Time = 460 meters / 18.89 m/s
Time ≈ 24.35 seconds
It will take the train approximately 24.35 seconds to completely cross the 140-meter-long bridge.
(33) A train of length 350 meters is running at a speed of 30 km/hr. How long does it take to cross a 50-meter-long tunnel?
Answer : 48.01 seconds
Explanation
In this problem, we are asked to find how long it takes for the train to cross a tunnel, not a bridge. However, the concept remains the same. We first need to determine the total distance that the train has to travel to completely cross the tunnel. This distance includes the length of the train and the length of the tunnel.
Total distance = Length of train + Length of tunnel Total distance = 350 meters + 50 meters Total distance = 400 meters
Next, we need to convert the train’s speed from kilometers per hour (km/hr) to meters per second (m/s) since we’re dealing with meters.
1 kilometer = 1000 meters 1 hour = 3600 seconds
So, to convert 30 km/hr to m/s:
30 km/hr * (1000 m/km) / (3600 s/hr) = 8.33 m/s (approximately)
Now, we can use the formula:
Time = Distance / Speed
Time to cross the tunnel = Total distance / Train’s speed Time = 400 meters / 8.33 m/s
Time ≈ 48.01 seconds
It will take the train approximately 48.01 seconds to completely cross the 50-meter-long tunnel.
(34) A train of length 600 meters is running at a speed of 78 km/hr. In how many seconds will it pass a pole standing near the railway track?
Answer : 27.67 seconds
Explanation
First, we need to convert the speed of the train from km/hr to m/s, since the length of the train is given in meters.
78 km/hr = 78 * 1000 m/hr (converting km to m) = 78000 m/hr (since 1 hour = 3600 seconds) = 78000/3600 m/s = 21.67 m/s (rounded to two decimal places)
Now, we need to find the time it takes for the train to pass a pole standing near the railway track, which is the same as the time it takes for the front of the train to travel a distance of 600 meters at a speed of 21.67 m/s.
Using the formula:
time = distance / speed
time = 600 / 21.67 time = 27.67 seconds (rounded to two decimal places)
Therefore, the train will pass the pole in approximately 27.67 seconds.
(35) A train of length 410 meters is running at a speed of 60 km/hr. How long does it take to cross a 190-meter-long platform?
Answer : 36 seconds
Explanation
The total distance that the train has to cover in order to completely cross the platform is the sum of the length of the train and the length of the platform. So, the total distance that the train has to cover is:
Distance = Length of train + Length of platform Distance = 410 meters + 190 meters Distance = 600 meters
Now, we need to convert the speed of the train from km/hr to m/s, since the distance is given in meters.
60 km/hr = 60 * 1000 m/hr (converting km to m) = 60000 m/hr (since 1 hour = 3600 seconds) = 60000/3600 m/s = 16.67 m/s (rounded to two decimal places)
We can now use the formula:
time = distance / speed
To find the time it takes for the train to completely cross the platform.
time = 600 / 16.67 time = 36 seconds (rounded to two decimal places)
Therefore, it takes 36 seconds for the train to completely cross the 190-meter-long platform.
