Speed of the train = (36 x 5)/18 = 10 m/sec.
Distance = (Time x Speed ) = (8 x 10 ) = 80 meters
? Length of the train = 80 meters
? Speed = Distance / Time = (300/15)
= 20 m/sec
= (20 x 18) / 5 = 72 km/hr
Relative speed = (25 + 2) = 27 km/hr = 27 x (5/18) m/sec. = 15/2 m/sec.
Time taken by the train to pass the men. = 270 / (15/2) = 36 sec.
Let the required speed be y km/hr.
Then, ( 2 x 64 ) x [ y / (64 + y)] = 56
? 128y = 64 x 56 + 56y
? y= (64 x 56 ) / 72
= 49.77 km/hr.
Speed of train in m/sec = (speed of train in km/hr) x 5/18
? speed of train in m/sec = 54 x 5/18 = 15 m/sec
Time taken to cross the tunnel = 2 minutes = 120 sec
Therefore, Total length covered by train in crossing the tunnel = Speed of train x Time taken to cross the tunnel
= 15 m/sec x 120 sec = 1800 m
Now, we know that
Total length covered by train in crossing the tunnel = Length of train + Length of tunnel
Given, Length of train =400m and
Calculated above, Length covered by train in crossing the tunnel = 1800 m
Therefore, Length of tunnel = 1800m- 400m = 1400m
We know that, when the trains are moving in the same direction,
Relative speed= Difference between the speed of train
and total distance for crossing each other = Sum of the length of train
Therefore, Relative speed = 72 km/hr - 54 km /hr = 18 km/hr
Relative speed in m/sec = 18 km/hr x 5/18 = 5 m/sec
and Total distance = 200m + 300m = 500m
and Total time taken to cross each other = Total distance in meter/ Relative speed in m/sec
= 500 m / (5 m/sec) = 100 sec
? Speed of the train = 60 x (5/18) m/sec = 50/3 m/sec
? Time taken by the train to cross the platform
= Time taken by it to cover (280 + 220) m
= (500 x 3/50) sec = 30 sec
? Speed of the train = 50 x (5/18) = 125/9 m/sec
? Time taken by the train to pass the pole = 250 x (9/125) = 18 sec
16 m/sec = 16 x (18/5) = 57.6 km/hr
180 km/hr = 180 x (5/18) = 50 m/sec
Since the sum of the length of the train and the length of the engine is needed, so both the lengths must be known.
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