Solution: Let the speed of train = x m/s
Distance travel by train to cross pole = Length of train , time = 15 sec
=> 15x = Length of train
Distance travel by train to cross platform = Length of train + Length of platform
= Length of train + 100,time = 25 sec
25x = 15 x + 100 => 25x – 15x = 100 => 10x = 100 => x = 100/10 = 10m/s
Length of train = 15x =15 x 10 = 150m
Do yourself: A train passes an electric pole in 10 seconds and a 130 m long platform in 20 seconds. How should I calculate the length of the train?
Q.2. A train 50 metres long passes a platform 100 metres long in 10 seconds. The speed of the train?
Solution: Distance travel by train to cross platform = Length of train + Length of platform = 50 + 100 = 150m,,time = 10 sec
Speed = d/t = 150/10= 15m/s
Q.3. A train moves with a speed of 108 km/h. Find Its speed in metres per second?
Solution: Speed = 108 x (1000m/3600sec) = 30m/s
Q.4. In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr?
Solution: Speed = 144 x (1000m/3600sec) = 40m/s
Distance travel by train to cross pole = Length of train = 100m
Time =distance / time = 100/40 = 2.5sec
Q.5. A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, Find the length of the train ?
Solution: Time = 10min = 10 x 60 = 600sec , distance = 12km = 12000m
Speed of train = 12000m/600sec = 20m/s
Length of train = Distance travel by train to cross a telegraph post = speed x time = 20 x 6 = 120m
Q.6. A train 110 metres long is running with a speed of 60 km/h. In what time will it pass a man who is running at 6 km/h in the direction opposite to that in which the train is going?
Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr = 66 x (5/18) m/s = 55/3m/s
Time taken to pass the man = Distance/speed = 110 m/ (55/3)m/s = (110x3)/55 = 6 sec
Q.7.Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 km/h and 45 km/h respectively. In how much time will they cross each other, if they are running in the same direction?
Solution: Relative speed of trains = (45 - 40) km/h = 5 km/h = 5 x(5/18 )m/s = 25/18m/s
Total distance covered = Sum of lengths of trains = 200 + 150 = 350 m.
Time taken = distance /speed = 350 /(25/18) = (350 x 18) /5 = 252 sec = 4 min 12sec