Raj likes to cross the moving train before it reaches a station 4 km away from where he is now. He starts from the end of the train and crosses it at a point 2.4 km away from the station. If he moves faster by 18 km/hr, he would cross the train at a point 3 km away from the station. If the train is moving with a speed of 54 km/hr, then what is the length of the train (in m)?
Raj likes to cross the moving train before it reaches a station 4 km away from where he is now. He starts from the end of the train and crosses it at a point 2.4 km away from the station. If he moves faster by 18 km/hr, he would cross the train at a point 3 km away from the station. If the train is moving with a speed of 54 km/hr, then what is the length of the train (in m)?
1). 450
2). 500
3). 550
4). 400
1 answers
Let their speed of the man be ‘x’ and the length of the train be ‘L’
⇒ Relative speed = x – 54
⇒ Time taken to cross = Length of train / Relative speed = L / (x – 54)
⇒ Distance travelled by the man in the same time = Speed × time
⇒ 4 – 2.4 = x × L/ (x – 54)
⇒ (1.6x – 86.4) /x = L → 1
In second case,
⇒ Relative speed = x + 18 – 54 = x – 36
⇒ Time taken to cross = Length of train / Relative speed = L / (x – 36)
⇒ Distance travelled by the man in the same time = Speed × time
⇒ 4 – 3 = (x + 18) × L/ (x – 36)
⇒ (x – 36) / (x + 18) = L → 2
Equating 1 and 2
⇒ (1.6x – 86.4) /x = (x – 36) / (x + 18)
⇒ 1.6x2 – 57.6x – 1555.2 = x2 – 36x
⇒ (0.6x2 – 21.6x – 1555.2) ÷ 0.6
⇒ x2 – 36x - 2592 = 0
Solving x = 72 or x = -36
Speed cannot be negative,
⇒ x = 72
Substituting in equation 2,
∴ L = 36/90 = 0.4 km = 400 m