Key Points to Remember:
a km/hr = a * (5/18) m/s
a m/s = a * (18/5) km/hr
Time taken by a train of length l metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover l metres.
Time taken by a train of length l metres to pass a stationary object of length b metres is the time taken by the train to cover ( l + b ) metres.
Suppose two trains or two bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed = u - v m/s.
Suppose two trains or two bodies are moving in the opposite direction at u m/s and v m/s, where u > v, then their relative speed = u + v m/s.
If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then the time taken by the train to cross each other = (a+b) / (u+v) s.
If two trains of length a metres and b metres are moving in same directions at u m/s and v m/s, then the time taken by the faster train to cross the slower train = (a+b) / (u-v) s.
If two trains start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then A's speed : B's speed = √b : √a
Practice Questions:
a km/hr = a * (5/18) m/s
a m/s = a * (18/5) km/hr
Time taken by a train of length l metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover l metres.
Time taken by a train of length l metres to pass a stationary object of length b metres is the time taken by the train to cover ( l + b ) metres.
Suppose two trains or two bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed = u - v m/s.
Suppose two trains or two bodies are moving in the opposite direction at u m/s and v m/s, where u > v, then their relative speed = u + v m/s.
If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then the time taken by the train to cross each other = (a+b) / (u+v) s.
If two trains of length a metres and b metres are moving in same directions at u m/s and v m/s, then the time taken by the faster train to cross the slower train = (a+b) / (u-v) s.
If two trains start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then A's speed : B's speed = √b : √a
Practice Questions:
Question 1:
A train 100 m long is running at the speed of 30 km/hr. Find the time taken to pass a man standing near the railway line.
Speed of the train = 30 * ( 5/18 ) m/s = 25/3 ms/s
Distance moved in passing the standing man = 100 m
Time Taken = Distance / Speed =u 100 / (25/3) = 100 * ( 3/25 ) = 12 sec
Speed of the train = 30 * ( 5/18 ) m/s = 25/3 ms/s
Distance moved in passing the standing man = 100 m
Time Taken = Distance / Speed =u 100 / (25/3) = 100 * ( 3/25 ) = 12 sec
Question 2:
A train is moving at a speed of 132 km/hr. If the length of the train is 110 metres, how long will it take to cross a railway platform 165 metres long?
Speed of the train = 132 km/hr = 132 * (5/18) m/s = 110/3 m/s
Distance covered in passing the platform = 110 + 165 m = 275 m
Time Taken = 275 / (110/3) = 275 * ( 3/110 ) = 15/2 = 7(1/2) sec
Speed of the train = 132 km/hr = 132 * (5/18) m/s = 110/3 m/s
Distance covered in passing the platform = 110 + 165 m = 275 m
Time Taken = 275 / (110/3) = 275 * ( 3/110 ) = 15/2 = 7(1/2) sec
Question 3:
A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.
Let the length of the train be x metres.
Then, the train covers x metres in 8 seconds and x+180 metres in 20 seconds.
=> x/8 = (x+180)/20
=> 20x = 8(x+180)
=> 5x = 2x + 360
=> 3x = 360
=> x = 120 m
Speed of the train = Distance / Speed = 120 / 8 m/s = 15 * (18/5) = 54 kmph
Question 4:
A train 150 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
Speed of the train relative to man = 68 - 8 = 60 kmph = 60 * (5/18) = 50/3 m/s
Time taken by the train to cross the man = Time taken by it to cover 150 m at 50/3 m/s
=> 150 * (3/50) = 9 sec
Question 5:
A train 220 m long is running with a speed of 59 kmph. In what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going?
A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.
Let the length of the train be x metres.
Then, the train covers x metres in 8 seconds and x+180 metres in 20 seconds.
=> x/8 = (x+180)/20
=> 20x = 8(x+180)
=> 5x = 2x + 360
=> 3x = 360
=> x = 120 m
Speed of the train = Distance / Speed = 120 / 8 m/s = 15 * (18/5) = 54 kmph
Question 4:
A train 150 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
Speed of the train relative to man = 68 - 8 = 60 kmph = 60 * (5/18) = 50/3 m/s
Time taken by the train to cross the man = Time taken by it to cover 150 m at 50/3 m/s
=> 150 * (3/50) = 9 sec
Question 5:
Two trains 137 metres and 163 metres in length are running towards each other on parallel lines, one at the rate of 42 kmph and another at 48 kmph. In what time will they be clear of each other from the moment they meet?
Relative Speed of the train = 48 + 42 kmph = 90 kmph = 90 * (5/18) = 25 m/s
Time taken to pass each other = Time taken to cover (137 + 163) metres at 25 m/s => 300 metres = 300/25 = 12 sec
Time to Think:Relative Speed of the train = 48 + 42 kmph = 90 kmph = 90 * (5/18) = 25 m/s
Time taken to pass each other = Time taken to cover (137 + 163) metres at 25 m/s => 300 metres = 300/25 = 12 sec
A train 220 m long is running with a speed of 59 kmph. In what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going?
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