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PROBLEMS ON TRAINS
Important Points :
1. Time taken by a train x meters long in passing a signal post or a pole
or a standing man = Time taken by the train to cover x meters.
2. Time taken by a train x meters long in passing a stationary object of length y
meters = Time taken by the train to cover (x + y) metres.
3. Suppose two trains or two bodies are moving in the same direction at u kmph and v kmph such that u > v, then their relative speed = (u - v) kmph.
4. If two trains of length x km and y km are moving in. the same direction at u kmph and )I
kmph, where u > v, then time taken by faster train to cross the slower train ={
(X+Y) / (U-V) }hrs.
5. Suppose two trains or two bodies are moving in opposite directions at u kmph and v
kmph. Then, their relative speed = (u + v) kmph.
6. If two trains of length x km and y km are moving in opposite directions at u kmph and v kmph, then: time taken by the trains to cross eachother
= (x + y)/ (u + v) hrs.
7. If two trains start at the same time from two points A and B towards each other and after crossing they take a and b hours in reaching B and A respectively.
Then, A's speed : B's speed = ( 1/b : 1/a).
8. x kmph = (x x 5/18)m/sec.
9. y metres/sec. = [y x 18/5 )km/hr.
Solved Problems
Ex. 1. Find the time taken by a train 180 m long, running at 72 kmph,in crossing an electric pole.
Sol. Speed of the train = (72 x 5/18) m/sec = 20 m/sec.
Distance moved in passing the pole = 180 m.
Required time taken = (180/20) sec = 9 sec.
Ex. 2. A train 140 m long is running at 60 kmph. In how much time wiU it pass a platform 260 m long?
Sol. Speed of the train = (60 x 5/18) m/sec =50/3m/sec.
Distance covered in passing the platform = (140 + 260) m = 400 m
:. Time taken = (400 x 3/50) see = 24 sec.
Ex. 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.
Sol. 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) x=120
:. Length of train = 120m.
Speed of train = (120/8) m/sec = 15 m/sec = [15 X 18/5 ] Kmph
= 54 Kmph.
Ex. 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 ?
Sol. Speed of the train relative to man = (68 - 8) kmph
= (60 x 5/18)m/see = 50/3 m/sec
Time taken by the train to cross the man = Time taken by it to cover 150 m at ( 50/3)m/sec
= (150 x 3/50 )sec = 9 sec.
Ex. 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?
Sol. Speed of the train relative to man = (59 + 7) kmph
= (66 x 5/18 ) m/sec = ( 55/3) m/sec.
Time taken by the train to cross the man
:. (x + y)/15 = 20 or x + y = 300 or y =(300 – 160) m = 140m.
:. Length of the platform = 140 m.
Ex. 9. A man sitting in a train which is traveling at 50 kmph observes that a goods train,
traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 150 m long, find its speed.
Sol. Relative speed = (150/9) m/sec =(150/ 9 x 18/5) kmph = 60 kmph.
:. Speed of goods train = (60 - 50) kmph = 10 kmph.
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