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PROBLEMS ON TRAINS -> IMPORTANT FORMULAE

1. a km/hr = [a * 5/18]m/s.
2. a m/s = [a * 18/5] km/hr.
3. Time taken by a trian 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.
4. 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.
5. 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 relatives speed = (u - v) m/s.
6. Suppose two trains or two bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s
7. If two trains of length a metres and b metres are moving in opposite directions at u
8. If two trains of length a metres and b metres are moving in the same direciton 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) sec.
9. If tow trains (or bodies) 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).*

1.	Two tain 100 metres and 120 metres long are running in the same direction with speeds of 72 km/hr and 54 km/hr. In how much time will the first train cross the second?
	Sol. Relative speed of the train = (72 - 54) km/hr = 18 km/hr = [18 * 5/18] m/sec = 5 m/sec. Time taken by the trains to cross each other = Time taken to cover (100 + 120) m at 5 m/sec = [220/5]sec = 44 sec.
2.	A train 220 m long is running with a speed of 59 kmph. In what time will it pas a man who is running at 7 kmph in the direction opposite to that in which the tain is going?
	Sol. Speed of the train relative to man = (59 + 7) kmph = [66 * 5/18] m/sec = [55/3] m/sec. Time taken by the train to cross the man = Time taken by it to cover 220m at [55/3] m/sec = [220 * 3/55] sec = 12 sec.
3.	A man siting in a trian which is travelling at 50 kmph observes that a goods trian, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.
	Sol. Relative speed = [280/9] m/sec = [280/9 * 18/5] kmph = 112 kmph. ∴ Speed of goods train = (112 - 50) kmph = 62 kmph.

31.	A speed of 14 metres per second is the same as :
	A. 50.4 km/hr B. 55 km/hr C. 60 km/hr D. 68.5 km/hr

Ans: A.

Sol.
14 m/sec = [14 * 18/5] km/hr = 50.4 km/hr.

32.	A man sitting in a train which is travelling at 50 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.
	A. 36 kmph B. 62 kmph C. 78 kmph D. 90 kmph

Ans: B.

Sol.
Relative speed = (280/9) m / sec
= (280 / 9 x 18/5)kmph = 112 kmph.
∴ Speed of goods train = (112 - 50) kmph = 62 kmph.

33.	How long does a train 110 metres long running at the speed of 72 km / hr take to cross a bridge 132 metres in length?
	A. 9.8 sec B. 12.1 sec C. 12.42 sec D. 14.3 sec

Ans: B.

Sol.
Speed = (72 x 5/18) m/sec.
Total distance covered = (110 + 132)m = 242 m.
∴ Required time = (242/20) sec = 12.1 sec.