Length of train = 120 m.
Total taken in crossing the pole = 10 seconds.
Speed of the train = length / time
= 120 / 10
= 12 m/s
= 12 x (18/5)
= 43.2 km/hr
Speed of train = (120/5) = 24 m/sec.
Time takes to cross the platform
= (120 + 180)/24
= 121/2
Speed of the train = 18 km/h = 18 x 5/18 m/s = 5 m/s
Distance covered = Length of the train = 120 m
? Time taken by the train to cross the man = Distance/Speed
= 120/5 = 24 s
Relative speed of train
= Speed of train + Speed of car
? 90 = Speed of train + 15
? Speed of train = 90 - 15 = 75 km/h
We know that, if two trains are running in the same direction, then relative speed is equal to the difference of the speeds of both the trains.
? Required relative speed = 21 - 15 = 6 km/h
When two trains are moving in opposite directions then their relative speed is equal to the sum of the speed of both the trains.
? Required relative speed = 6 + 12 = 18 m/s
Let the required distance be x km.
Then, ( x/80 ) - ( 220 - x ) / 100 = 1/2
? 5x - 4( 220 - x ) = 200
? 9x = 1080
? x = 120 km
? Required distance = 120 km
Suppose they meet x km. from X
Then, x/20 = (500 - x)/30
? 30x = 10000 - 20x
? x = 200 km.
Let the speed of the train be Y km/hr
? length of the train = 150 m
= 150/1000 = 3/20 km.
Time taken to cross the man = 10 seconds
= 10/ (60 x 60) = 1/360 hrs .
? time = Length of the train /( speed of the train - speed of the man )
? 1/360 = ( 3 / 20) / ( Y - 2)
? (Y - 2 ) = 3/20 x 360
? (Y - 2 )= 54
? Y = 54 + 2
= 56 km/hr.
? Speed = (45 x 5/18) = (25/2) m/sec
Distance = (Time x Speed) = (12 x 25 / 2 ) meters
= 150 meters
? Length of the train = 150 meters
? Speed of the train = 20 x (5/18) = (50/9) m/sec
? Time taken by the train to pass the man = 75 x (9/50) = 13.5 sec
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