The speed of a train is 78 km/h. It crosses a tunnel in 45 seconds overtakes a person walking at a speed of 6 km/h, in the same direction, in 15seconds. The length (in m) of the tunnel is:

675

Total distance = Length of Train + Length of tunnel

Speed = 78 km/h

78 km/h = 78 × \(\frac{5}{18}\) = \(\frac{65}{3}\) m/sec

Distance = Speed × Time = \(\frac{65}{3}\) × 45 = 975 m

Train crosses a man in 15 sec .

Relative speed ( moves in same direction ) = 78 - 6 = 72 km/h

= 20 m/sec

Length of train = 20 × 15 = 300 m

975 = Length of Train + Length of tunnel 

975 = 300 + Length of tunnel 

Length of tunnel = 675 m