Wednesday, January 29, 2014
PROBLEMS ON TRAINS
IMPORTANT FACTS AND FORMULAE
1. a km/hr= (a* 5/18) m/s.
2. a m / s = (a*18/5) km/hr.
3 Time taken by a train of length 1 metres to pass a
pole or a standing man or a signal post is
equal to the time taken by the train to cover 1 metres.
4.
Time taken by a train of length 1 metres to pass a stationary object of
length b metres is the time taken
by the train to cover (1 + 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 m
/ s and v m/s, then time taken by the trains to cross each other
= (a + b)/(u+v) sec.
8.If two trains of
length a metres and b metres are
moving in the same direction
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 two 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 speet) :
(B’s speed) = (b1/2: a1/2).
SOLVED EXAMPLES
Ex.I.
A train 100 m long is running at the speed of 30 km / hr. Find the time taken by it to pass a man standing near the railway line. (S.S.C.
2001)
Sol. Speed of the train = (30 x 5/18_) m / sec = (25/3) m/
sec.
Distance moved in passing the
standing man = 100 m.
Required time taken = 100/(25/3) =
(100 *(3/25)) sec = 12 sec
Ex. 2. A train is moving
at a speed of 132 km/br. If the length of the train is
110
metres, how long will it take to cross a railway platform 165
metres long?
(Section
Officers', 2003)
Sol. Speed of train = 132
*(5/18) m/sec = 110/3 m/sec.
Distance
covered in passing the platform = (110 + 165) m = 275 m.
Time taken =275
*(3/110) sec =15/2 sec = 7 ½ 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 sec
x/8=(x+180)/20 รณ 20x = 8 (x + 180) <=> x = 120.
Length of the train = 120 m.
Speed of
the train = (120/8) m / sec = m / sec = (15 *18/5) kmph
= 54 km
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* 5/18) m/sec = (50/3)m/sec
Time taken by the train to cross the man I
= Time taken by It to cover 150 m at 50/3 m / sec = 150 *3/ 50 sec = 9sec
Ex. 5. A train 220 m long is running with a speed of 59 kmph.. In what 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
*5/18 m/sec = 55/3 m/sec.
Time taken by the train to cross the man
= Time taken by it to cover 220 m at (55/3) m / sec
= (220 *3/55) sec = 12 sec
Ex. 6. 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 kmpb. In what time
will they be clear of each other from the moment they meet?
Sol.
Relative speed of the trains = (42 + 48) kmph = 90 kmph
=(90*5/18)
m / sec = 25 m /sec.
Time
taken by the trains to'pass each other
= Time taken to cover (137
+ 163) m at 25 m /sec =(300/25) sec = 12 sec
Ex. 7. Two trains 100
metres and 120 metres long are
running in the same direction with speeds of 72 km/hr,In howmuch time
will the first train cross the second?
Sol:
Relative speed of the trains = (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.
Ex. 8. A train 100 metres long takes 6 seconds to cross a man
walking at 5 kmph in the direction opposite
to that of the train. Find the speed of the train.?
Sol:Let the
speed of the train be x kmph.
Speed of
the train relative to man = (x + 5) kmph = (x + 5) *5/18 m/sec.
Therefore 100/((x+5)*5/18)=6 <=> 30 (x + 5) = 1800
<=> x = 55
Speed of the train is 55 kmph.
Ex9. A train running at 54 kmph takes
20 seconds to pass a platform. Next it takes.12 sec to pass a man walking at 6 kmph in the same direction
in which the train is going . Find the length of the train and the length of
the platform.
Sol:Let the length of train be x metres and length of platform be y metres.
Speed of the train relative to man = (54 - 6) kmph = 48 kmph
= 48*(5/18) m/sec = 40/3 m/sec.
In passing a man, the train covers its own
length with relative speed.
Length of train = (Relative
speed * Time) = ( 40/3)*12 m = 160 m.
Also, speed
of the train = 54 *(5/18)m / sec = 15 m / sec.
(x+y)/15 = 20
<=> x + y = 300 <=> Y = (300 - 160) m = 140 m.
Ex10. 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 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.
