(11) Two trains of lengths 600 meters and 700 meters are running on parallel lines in the same direction at 70 km/hr and 90 km/hr. In how many seconds will the faster train pass the slower train?
Answer : 233.81 seconds
Explanation
To determine how long it will take for the faster train to pass the slower train, we need to find the relative speed between them and the distance that needs to be covered.
First, we need to convert the speeds from kilometers per hour (km/hr) to meters per second (m/s).
1 km/hr = 1000 m/km * 1 hr/3600 s = 5/18 m/s
So, the speeds of the trains in meters per second are:
Train 1 (slower train) = 70 km/hr * 5/18 m/s = 350/18 m/s ≈ 19.44 m/s Train 2 (faster train) = 90 km/hr * 5/18 m/s = 450/18 m/s ≈ 25 m/s
Now, we calculate the relative speed between the trains:
Relative speed = Speed of Train 2 – Speed of Train 1 Relative speed ≈ 25 m/s – 19.44 m/s ≈ 5.56 m/s
The total length of the trains is:
Total length = Length of Train 1 + Length of Train 2 Total length = 600 m + 700 m = 1300 m
Now, we can use the formula time = distance / speed to calculate the time it takes for the faster train to pass the slower train:
Time = Total length / Relative speed Time ≈ 1300 m / 5.56 m/s ≈ 233.81 seconds
It will take approximately 233.81 seconds for the faster train to pass the slower train.
(12) A train of length 420 meters is running at a speed of 84 km/hr. How long does it take to cross a 180-meter-long bridge?
Answer : 25.73 seconds
Explanation
To determine how long it will take for the train to cross the bridge, we first need to convert the train’s speed from kilometers per hour (km/hr) to meters per second (m/s).
1 km/hr = 1000 m/km * 1 hr/3600 s = 5/18 m/s
So, the speed of the train in meters per second is:
Train speed = 84 km/hr * 5/18 m/s = 420/18 m/s = 23.33 m/s
Now, we need to calculate the total distance the train needs to travel to cross the bridge completely. This is the sum of the train’s length and the bridge’s length:
Total distance = Train length + Bridge length Total distance = 420 m + 180 m = 600 m
Now, we can use the formula time = distance / speed to calculate the time it takes for the train to cross the bridge:
Time = Total distance / Train speed Time = 600 m / 23.33 m/s ≈ 25.73 seconds
It will take approximately 25.73 seconds for the train to cross the 180-meter-long bridge.
(13) A train of length 550 meters is running at a speed of 50 km/hr. How long does it take to cross a 350-meter-long tunnel?
Answer : 64.8 seconds
Explanation
To cross the tunnel, the train will need to cover a distance equal to the length of the tunnel plus the length of the train. Therefore, the total distance to be covered by the train is:
Total distance = length of train + length of tunnel = 550 + 350 = 900 meters
We know that the speed of the train is 50 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 = 50 km/hr = 50 x (5/18) m/s = 125/9 m/s
Now, we can use the formula:
time = distance / speed
To find the time taken by the train to cross the tunnel.
time = 900 / (125/9) = 64.8 seconds (approx)
Therefore, it will take approximately 64.8 seconds for the train to cross a 350-meter-long tunnel.
(14) A train of length 600 meters is running at a speed of 90 km/hr. In how many seconds will it pass a pole standing near the railway track?
Answer : 24 seconds
Explanation
To pass the pole standing near the railway track, the train will need to cover a distance equal to its own length. Therefore, the total distance to be covered by the train is:
Total distance = length of train = 600 meters
We know that the speed of the train is 90 km/hr. To calculate the time taken by the train to pass the pole, we need to convert the speed from km/hr to m/s.
Speed of train = 90 km/hr = 90 x (5/18) m/s = 25 m/s
Now, we can use the formula:
time = distance / speed
To find the time taken by the train to pass the pole.
time = 600 / 25 = 24 seconds
Therefore, it will take 24 seconds for the train to pass a pole standing near the railway track.
(15) Two trains are running on parallel lines in the same direction at 45 km/hr and 65 km/hr. The faster train takes 2 minutes to pass the slower train. What is the length of the slower train?
Answer : 167 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 = (65 – 45) km/hr = 20 km/hr = 20 x (5/18) m/s = 50/9 m/s
We also know that the faster train takes 2 minutes to pass the slower train. Therefore, we can write:
(L1 + L2) / (50/9) = 120 seconds
Simplifying this equation, we get:
L1 + L2 = (50/9) x 120
L1 + L2 = 667 meters
We know that the length of the faster train is 500 meters. Therefore, we can substitute the value of L2 in the above equation to get:
L1 + 500 = 667
L1 = 167 meters
Therefore, the length of the slower train is 167 meters.
