A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:

Step 1: Understand the given data

• Length of train = 800 meters
• Speed of train = 78 km/hr
• Time to cross the tunnel = 1 minute = 60 seconds

Step 2: Convert speed to meters per second

Speed in m/s = 78 × (5/18) = 21.67 m/s

Step 3: Use the formula: Distance = Speed × Time

Total distance covered in 60 seconds = 21.67 × 60 = 1300 meters

Step 4: Calculate the length of the tunnel

Distance = Length of train + Length of tunnel

1300 = 800 + Length of tunnel

Length of tunnel = 1300 - 800 = 500 meters

Answer: 500 meters

The length of the tunnel is 500 meters.

This problem demonstrates the use of basic motion formulas where a train covers its own length plus the length of the tunnel in the given time. Converting the train’s speed to m/s ensures consistency in units for calculating distance accurately.