Problems on Trains Online Test 2

Speed of the train = 12.5 km/hr
Speed of girl = 1 km/hr
Relative speed = speed of train + speed of girl
= (12.5 + 1) km/hr
= 13.5 km/hr
Convert km/hr into m/s
13.5 km/hr = ( 13.5 * 5 /18)m/s
= 67.5 / 18 m/s
= 3.75 m/s
Time = distance / speed
Time taken by the train to pass the man = 135 / 3.75
= 36 sec.

Relative speed = distance / time
= (140 / 4.5) m/s
= 31.11 m/s
Convert m/s into km/hr
31.11 m/s = (31.11 * 18 / 50 km/hr
= (560 / 5) km/hr
= 112 km/hr
Relative speed = speed of train + speed of train (by sitting)
speed of train = Relative speed – speed of train (by sitting)
= (112 – 25) km/hr
= 87 km/hr
Therefore the speed of goods train is 87 km/hr

Length of the train = 200 m
Man walking speed = 10 km/hr
Let the speed of the train be ‘x’ km/hr
Speed of the train relative to man = (x +10) km/hr
Convert km/hr into m/s
(x +10)km/hr = (x + 10) * 5 / 18 m/s
Speed = distance / time
200 / (x + 10)* 5 / 18 = 12
18 * 200 / 5(x + 10) = 12
3600 = 60(x +10)
3600 = 60x +600
60x = 3000
X = 50
So speed of the train is 50 km/hr

Speed of the train = 136 km/hr
Speed of boy = 6 km/hr
Speed of the train relative to boy = (13 + 6)km/hr
= 142 km/hr
Convert km/hr into m/s 142 km /hr = (142 * 5 / 18)
= 710 / 18 m/s
= 39.44 m/s
Time taken by the train to cross a boy = time taken bt it to cover 300 m at 39.44 m/s
=300 / 39.44 [speed time= distance / speed]
= 7.6 sec

Speed of the train = 30 km/hr
Speed of man = 3 km/hr
Length of the train = 165m
If direction is given in opposite direction then we add both speed.
That is (30 + 3 )= 33 km/hr
Convert km/hr into m/s
33km /hr = (33 * 5 / 18) m/s = 55/6 m/s
If the train time taken to passing a man who running in opposite direction
That is 55/6 m/s
So we can easily get the distance of m/s
So it cover 165 m
i.e., 165 * 6 /55 = 18 sec.

Length of the train = 330 m
Speed = distance / time.
Speed of the train relative to man = 330 / 18 m/s
= 110 / 6 m/s
Convert m/s into km/hr
Therefore 110 / 6 m/s = (110 / 6 * 18 / 5) km/hr
= 22 * 3 km/hr
= 66 km/hr
Let the speed of the train be ‘x’ km/hr
Relative speed = (x +18) = 66 km/hr
X + 18 = 66
X = 48
Therefore the speed of the train is 48 km/hr

Length of the train = 400m
Speed of train = 124 km/hr
Speed of person = 40 km/hr
Relative speed (speed of trai relative to man) = (124 + 40) km/hr
= 164 km/hr
[As the train and the running person are moving in opposite direction,therir speed values are added to find
the relative speed.]
Convert km/hr into m/s
164 km/hr = 164 * 5 / 18
= 820/18
= 45.55 m/s
We know speed = distance / time
Therefore time taken by the train to cross the running person = time taken by the train to cover 400m at a
relative of 45.55 m/s
= 400 / 45.55
= 8.78 sec.

We know as the train and the running person are moving in opposite direction,therir speed values are added
to find the relative speed.
Relative speed = speed of mail train + speed of running engine
= (120 +12)km/hr
= 132 km/hr
Convert km/hr into m/s
132 km/hr = (132 * 5 /18) m/s
= (660 / 18)m/s
= 36.66 m/s
Time taken by train to pass a man = distance / speed
[ from the length of the mail train is the distance]
= 220 / 36.66
= 6 sec.

Speed of person = 10km/hr
As the train and the running person are moving in opposite direction,therir speed values are added to find
the relative speed.
Relative speed = speed of train + speed of person
25 = speed of train
Speed of train = 25 – 10
= 15 km/hr
Convert km/hr into m/s
15 km/hr = (15 * 5 / 18)m/s
= 25 / 6 m/s
Distance = speed * time
= 25 / 6 * 10
= 250/6 m/s
= 41.6 m

Length of the train = 110 m
Speed of the train = 30 km/hr
Speed of the boy = 3.5 km/hr
Speed of the train relative to man = (30 + 3.5) km/hr
= 33.5 km/hr
Convert km/hr into m/s
33.5 km/hr = (33.5 * 5 /18) m/s
= 167.5 / 18
= 9.30 m/s
Time taken by the train to cross the man = time taken by it to cover 110 m at 9.30 m/s
= 110 / 9.30
= 11.8 seconds
= 12 sec(approx.)