Question
Train A and B can cross a 350 meters long platform in
the same time. The length of Train A is 250 meters and the speed of Train B is 3/2 times the speed of Train A. If Train A crosses a bridge of the same length as of Train B in 50 seconds, then find the time (in seconds) taken by Train B to cross a tunnel 230 m long.Solution
ATQ, vA = speed of Train A, LB = length of Train B, vB = speed of Train B Same time to cross 350 m platform: (250 + 350)/vA = (LB + 350)/vB vB = (3/2) vA 600/vA = (LB + 350)/((3/2) vA) 600 = (2/3)(LB + 350) 1800 = 2(LB + 350) 900 = LB + 350 LB = 550 m Bridge length = LB = 550 m Train A over bridge distance = 250 + 550 = 800 m Time = 50 s vA = 800/50 = 16 m/s vB = (3/2)*16 = 24 m/s Tunnel length = 230 m Train B over tunnel distance = 550 + 230 = 780 m Time = 780/24 = 32.5 s
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