The length of train A is x+10 meters and length of train B is x+20 meters respectively. Both trains cross each other is 11/2 seconds and speed of train A is 90 km/hr. The speed of train B is 40% more than that of train A, then find the time taken by the train B to cross a 110 meters long platform (in seconds)?

Explanation

Information Given: Length of train A = x + 10 meters Length of train B = x + 20 meters Both trains cross each other in 11/2 seconds (5.5 seconds) Speed of train B is 40% more than speed of train A Asked: Time taken by train B to cross a 110 meters long platform Concept/Formula Used: When two trains cross each other, distance = sum of their lengths Relative speed = sum of their speeds Speed of B = 1.4 × speed of A Time = distance / speed Time taken by B to cross platform = (length of train B + platform length)/speed of B Explanation: Convert speed of train A to m/s: 90 km/hr = (90 × 5) / 18 = 25 m/s Speed of train B = 40% more than A = 1.4 × 25 = 35 m/s Total length when crossing each other = (x + 10) + (x + 20) = 2x + 30 meters Relative speed = 25 + 35 = 60 m/s Time given to cross each other = 5.5 seconds Distance = speed × time = 60 × 5.5 = 330 meters So, 2x + 30 = 330 2x = 300 x = 150 meters Length of train B = x + 20 = 150 + 20 = 170 meters Length of platform = 110 meters Total distance for B to cross platform = 170 + 110 = 280 meters Speed of train B = 35 m/s Time for B to cross platform = Distance/Speed = 280 / 35 = 8 seconds