Two men are running in the same direction with a speed of 6 km per hour and \(7\frac{1}{2}\) m km per hour. A train running in the same direction crosses in 5 sec and \(5\frac{1}{2}\) sec respectively. The length and the speed of the train are respectively.
Two men are running in the same direction with a speed of 6 km per hour and \(7\frac{1}{2}\) m km per hour. A train running in the same direction crosses in 5 sec and \(5\frac{1}{2}\) sec respectively. The length and the speed of the train are respectively.
1). 22.92 m (approximately) and 22 km/hour
2). 82.5 m (approximately) and 22.5 km/hour
3). 22.90 m (approximately) and 20.5 km/hour
4). 22.92 m (approximately) and 22.5 km/hour
1 answers
Given,
Men 1 speed = 6 km/h
Men 2 speed = 15/2 km/h
Then,
Let the speed of train be M km and the length of the train be N meter.
Speed of train relative to men 1 = (M – 6) km/h = 1000(M – 6)/3600 m/s
Time taken to pass the man 1 = 5 sec
⇒ 5 = N / 1000(M – 6)
Speed of train relative to men 2 = (M – 15/2) km/h = 1000(M – 15/2)/3600 m/s
Time taken to pass man 2 = 11/2 sec
⇒ 11/2 = N / 1000(M – 15/2)
Solving equations,
⇒ 5/(11/2) = (M – 15/2)/(M – 6)
⇒ 10/11 = (2M – 15)/(2M – 12)
⇒ 20M – 120 = 22M – 165
⇒ M = 45/2 = 22.5km/h
Speed of train = 22.5 km/h
Then,
⇒ N = 5 × 1000 × (22.5 – 6)/3600
⇒ N = 22.92 m
∴ Length of train = 22.92 mOther Questions
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