Trains A and B have lengths l and 4l and enter a tunnel of length L from opposite directions with speeds 108 km h⁻¹ and 72 km h⁻¹. Train A takes 35 s less than B to cross the tunnel. Given L = 60l, the tunnel length is:
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Question

Trains A and B have lengths l and 4l and enter a tunnel of length L from opposite directions with speeds 108 km h⁻¹ and 72 km h⁻¹. Train A takes 35 s less than B to cross the tunnel. Given L = 60l, the tunnel length is:

Options

G1 Physics · Accepted Answer

Convert speeds: 108 km h⁻¹ = 30 m s⁻¹ 72 km h⁻¹ = 20 m s⁻¹ Times to clear tunnel: Tₐ = (L+l)/30 Tʙ = (L+4l)/20 Given Tʙ - Tₐ = 35 and L=60l: 64l/20 - 61l/30 = 35 (192-122)l/60 = 35 70l/60 = 35 l = 30 m Therefore, L = 60l = 1800 m Hence option B follows.