Train Crossing a Tunnel: Formula and Solved Questions

Train Crossing a Tunnel problems require the train to cover its own length plus the tunnel length. The basic relation is distance = speed × time. For a train of length L crossing a tunnel of length T, distance covered is L + T, so time = (L + T) ÷ speed after using consistent units.

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What Is Train Crossing a Tunnel?

A train crossing a tunnel means the train must completely pass through the tunnel, so its front travels the combined length of the train and the tunnel.

If the train length is L and the tunnel length is T, the required distance is L + T. Therefore, time = (L + T) / v, where v is the train speed in the same distance unit per unit time. For example, a 150 m train crossing a 350 m tunnel covers 500 m in total.

Train Crossing a Tunnel Formula & Tricks

Important Formulas

Time to cross a tunnel
Time = (Train length + Tunnel length) / Speed

Use this when the train and tunnel lengths and the train speed are known.

Distance covered
Distance = Train length + Tunnel length

The train has completely crossed only when its rear end leaves the tunnel.

Tunnel length
Tunnel length = Speed × Time − Train length

Use this when crossing time, speed and train length are given.

Speed conversion
Speed in m/s = Speed in km/h × 5/18

Convert km/h to m/s when lengths are given in metres and time is required in seconds.

Speed from distance and time
Speed = (Train length + Tunnel length) / Time

The resulting speed has the distance unit divided by the time unit used.

Quick Tricks

Add both lengths before dividing

For a tunnel, do not use the tunnel length alone. The train front must travel the tunnel length and then the train's own length before the rear clears the tunnel.

Example: For a 120 m train and a 480 m tunnel, total distance is 120 + 480 = 600 m.
Use one unit system

Convert speed to m/s for metre-second data, or convert lengths to kilometres when speed is in km/h. This prevents unit errors.

Example: 54 km/h = 54 × 5/18 = 15 m/s.
Use the difference of crossing times

For the same train and speed, the extra time taken to cross a tunnel compared with a pole equals tunnel length divided by speed.

Example: If a train takes 8 seconds to cross a pole and 28 seconds to cross a tunnel at 20 m/s, tunnel length = 20 × (28 − 8) = 400 m.

Train Crossing a Tunnel Concepts

Distance Required for Complete Crossing

A train completely crosses a tunnel after covering the sum of the train length and tunnel length.

At the starting instant, the train front is at the tunnel entrance. At the finishing instant, the train rear is at the tunnel exit. The front therefore travels T + L, where T is tunnel length and L is train length.

Example: A 200 m train crosses a 600 m tunnel. Required distance = 200 + 600 = 800 m.

Finding Crossing Time

Crossing time is obtained by dividing the combined length by the train speed.

First convert the speed into a unit compatible with the lengths. Then apply t = (L + T) / v. If L and T are in metres and v is in m/s, the answer is in seconds.

Example: A 180 m train crosses a 420 m tunnel at 15 m/s. Time = (180 + 420) / 15 = 600 / 15 = 40 seconds.

Finding Tunnel Length

Tunnel length equals the distance travelled during crossing minus the train length.

Calculate the distance as speed multiplied by time, then subtract the train length: T = vt − L. The speed and time must produce a distance in the same unit as L.

Example: A 25 m/s train takes 32 seconds to cross a tunnel and is 200 m long. Tunnel length = 25 × 32 − 200 = 800 − 200 = 600 m.

Comparing Pole and Tunnel Crossings

A train crossing a pole covers only its own length, while crossing a tunnel requires its length plus the tunnel length.

For the same train and speed, pole-crossing time is L/v and tunnel-crossing time is (L + T)/v. Their time difference is T/v, so T = v × (tunnel time − pole time).

Example: At 18 m/s, a train takes 10 seconds to cross a pole and 30 seconds to cross a tunnel. Tunnel length = 18 × (30 − 10) = 360 m.

Train Crossing a Tunnel Video Lessons

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Trains: Tunnels, Time Gaps and Meeting Points

Learn how to solve train problems involving tunnel crossings, time gaps between trains, and meeting points using time, speed, distance, and relative speed concepts.

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Practice Train Crossing a Tunnel Questions

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Quick Revision Notes

Train Crossing a Tunnel: Quick Revision

Use these direct rules for calculation-based questions.

  • Complete tunnel crossing distance = train length + tunnel length.
  • Time = (train length + tunnel length) / speed.
  • Tunnel length = speed × time − train length.
  • Convert km/h to m/s by multiplying by 5/18.
  • Convert m/s to km/h by multiplying by 18/5.
  • A train crossing a pole covers only its own length.
  • For the same train and speed, tunnel time − pole time = tunnel length / speed.
  • Keep length, speed and time units consistent before applying a formula.

Train Crossing a Tunnel FAQs

What is the train tunnel formula?

The formula is Time = (Train length + Tunnel length) / Train speed. The train must cover both lengths for complete crossing.

A 250 m train crosses a 750 m tunnel at 20 m/s. What is the crossing time?

Total distance = 250 + 750 = 1,000 m. Time = 1,000 / 20 = 50 seconds.

How do you find tunnel length from crossing time?

Use Tunnel length = Speed × Time − Train length. For example, at 18 m/s for 40 seconds with a 220 m train, tunnel length = 720 − 220 = 500 m.

Why is train length added to tunnel length?

The front of the train must reach the tunnel exit, and the rear must also leave the tunnel. Thus, the front travels the tunnel length plus the train length.

A train travels at 72 km/h. What is its speed in m/s?

72 × 5/18 = 20 m/s. This conversion is required when lengths are in metres and time is in seconds.

What is the difference between crossing a pole and crossing a tunnel?

For a pole, distance covered is only the train length. For a tunnel, distance covered is train length + tunnel length.

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