(36) Two trains of lengths 510 meters and 610 meters are running on parallel lines in the opposite direction at 65 km/hr and 75 km/hr. In how many seconds will the trains pass each other?
Answer : 28.81 seconds
Explanation
We need to find the time taken by the two trains to pass each other. When two trains of lengths L1 and L2, running at speeds v1 and v2 in opposite directions, pass each other, the distance covered by the two trains is equal to the sum of their lengths (L1 + L2).
In this case, the two trains have lengths 510 meters and 610 meters and are running in opposite directions at speeds 65 km/hr and 75 km/hr respectively. We need to convert these speeds to m/s:
Speed of the first train (v1) = 65 km/hr = (65 * 1000) / (60 * 60) m/s = 18.06 m/s (rounded to two decimal places)
Speed of the second train (v2) = 75 km/hr = (75 * 1000) / (60 * 60) m/s = 20.83 m/s (rounded to two decimal places)
Total distance covered by the two trains = sum of their lengths = (510 + 610) meters = 1120 meters.
Relative speed of the two trains = (v1 + v2) m/s = (18.06 + 20.83) m/s = 38.89 m/s (rounded to two decimal places)
Now, we can use the formula:
time = distance / relative speed
To find the time taken by the two trains to pass each other:
time = 1120 / 38.89 time = 28.81 seconds (rounded to two decimal places)
Therefore, the two trains will pass each other in approximately 28.81 seconds.
(37) Two trains of equal length are running on parallel lines in the opposite direction at 60 km/hr and 90 km/hr. The trains pass each other in 40 seconds. The length of each train is?
Answer : 83.84 meters
Explanation
When two trains of equal length pass each other, the total distance covered by the two trains is equal to twice the length of one train (2L).
In this case, the two trains are running in opposite directions at speeds of 60 km/hr and 90 km/hr respectively. We need to convert these speeds to m/s:
Speed of the first train = 60 km/hr = (60 * 1000) / (60 * 60) m/s = 16.67 m/s (rounded to two decimal places)
Speed of the second train = 90 km/hr = (90 * 1000) / (60 * 60) m/s = 25 m/s
The total distance covered by the two trains in 40 seconds is:
Distance = Relative Speed * Time Distance = (Speed of the first train + Speed of the second train) * Time Distance = (16.67 + 25) * 40 Distance = 167.68 meters (rounded to two decimal places)
Since the total distance covered is equal to twice the length of one train, we have:
2L = 167.68 L = 167.68 / 2 L = 83.84 meters (rounded to two decimal places)
Therefore, the length of each train is approximately 83.84 meters.
(38) A train of length 560 meters is running at a speed of 100 km/hr. How long does it take to cross a 260-meter-long station?
Answer : 29.52 seconds
Explanation
The total distance that the train has to cover in order to completely cross the station is the sum of the length of the train and the length of the station. So, the total distance that the train has to cover is:
Distance = Length of train + Length of station Distance = 560 meters + 260 meters Distance = 820 meters
Now, we need to convert the speed of the train from km/hr to m/s, since the distance is given in meters.
100 km/hr = 100 * 1000 m/hr (converting km to m) = 100000 m/hr (since 1 hour = 3600 seconds) = 100000/3600 m/s = 27.78 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 260-meter-long station.
time = 820 / 27.78 time = 29.52 seconds (rounded to two decimal places)
Therefore, it takes 29.52 seconds for the train to completely cross the 260-meter-long station.
(39) Two trains are running on parallel lines in the same direction at 20 km/hr and 40 km/hr. The faster train takes 180 seconds to pass the slower train. What is the length of the faster train?
Answer :
Explanation
The relative speed of the two trains is 40 km/hr – 20 km/hr = 20 km/hr. Converting this to meters per second:
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 180 seconds to pass the slower train. During this time, it covers the combined length of both trains (L1 + L2) at the relative speed:
Distance = Relative speed * Time L1 + L2 = 5.56 m/s * 180 s L1 + L2 = 1000.8 m
This distance (1000.8 m) is the combined length of both trains when the faster train fully passes the slower train. However, we do not have enough information to determine that the trains are of equal length.
To find the length of the faster train, we would need additional information about the lengths of the trains or their ratio.
(40) Two trains of lengths 700 meters and 800 meters are running on parallel lines in the same direction at 50 km/hr and 70 km/hr. In how many seconds will the faster train pass the slower train?
Answer : 270 seconds
Explanation
Let’s find the relative speed of the two trains. Since they are moving in the same direction, we subtract the speed of the slower train from the speed of the faster train:
Relative speed = 70 km/hr – 50 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
The faster train needs to cover the combined length of both trains in order to pass the slower train. The combined length is:
L1 + L2 = 700 m + 800 m = 1500 m
Now, we can find the time it takes for the faster train to pass the slower train by dividing the combined length by the relative speed:
Time = Distance / Relative speed Time = 1500 m / 5.56 m/s ≈ 269.78 seconds
Therefore, it takes approximately 270 seconds (rounded to the nearest whole number) for the faster train to pass the slower train.
