Train Crossing a Bridge with Speed and Time Examples
Train Crossing a Bridge problems use the total distance covered by the train, which is the sum of the train’s length and the bridge’s length. The main relation is time = total distance ÷ speed. This page explains the formula, unit conversion, methods for finding unknown values and solved train crossing a bridge examples.
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What Is Train Crossing a Bridge?
If the train has length L metres, the bridge has length B metres and the speed is v metres per second, then t = (L + B) ÷ v. The train is considered to have crossed the bridge only when its rear end leaves the bridge. For speed in kilometres per hour, first convert it using v m/s = v × 5/18.
Train Crossing a Bridge Video Lessons
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Trains Crossing Platforms and Bridges
Understand how to calculate the time taken by a train to cross a platform or bridge using train length, structure length, and speed.
Train Crossing a Bridge Formula & Tricks
Important Formulas
The train must cover its own length L and the bridge length B for the complete train to leave the bridge.
Use this when L and B are in metres and v is in metres per second.
Convert kilometres per hour to metres per second before using lengths in metres.
If speed v, time t and train length L are known, subtract the train length from the total distance.
If speed v, time t and bridge length B are known, subtract the bridge length from the total distance.
Quick Tricks
For a bridge, do not use only the bridge length. Add the train length because the rear end must also travel across the bridge.
When lengths are in metres and speed is in km/h, multiply the speed by 5/18. This avoids unit mismatch.
First calculate vt, the total distance travelled. Then subtract the known length to find the unknown train or bridge length.
Train Crossing a Bridge Concepts
Combined Length of Train and Bridge
If the train length is L and the bridge length is B, the required distance is D = L + B. The front of the train travels across the bridge first, while the rear travels an additional distance equal to the train’s length before the crossing is complete.
Speed and Unit Conversion
For lengths in metres, express speed in metres per second. Use 1 km/h = 5/18 m/s and 1 m/s = 18/5 km/h. Then apply t = (L + B)/v.
Finding Time to Cross a Bridge
Use t = (L + B)/v after converting all quantities to compatible units. If speed is given in km/h and the total distance is in metres, either convert speed to m/s or convert distance to kilometres.
Finding an Unknown Length
The total distance travelled in time t at speed v is vt. Thus, bridge length B = vt − L, while train length L = vt − B. Keep v in metres per second when lengths are in metres.
Difference Between Crossing a Bridge and a Point
For a bridge, distance = L + B. For a pole, signal, or stationary person, distance = L because the object has no length considered in the calculation.
Train Crossing a Bridge Data Table
Use the structured data below while following the explanation and examples.
Distance Used in Different Train-Crossing Cases
The distance depends on the length of the object being crossed.
| Object crossed | Distance covered | Example for a 120 m train |
|---|---|---|
| Pole or person | Train length | 120 m |
| Bridge | Train length + bridge length | 120 m + bridge length |
| Platform | Train length + platform length | 120 m + platform length |
Note: Use time = distance ÷ speed after converting speed and distance to compatible units.
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Train Crossing a Bridge Revision Points
Use these formulas and rules for quick revision.
- Complete crossing distance = train length + bridge length.
- Time = (train length + bridge length) ÷ speed.
- Convert km/h to m/s by multiplying by 5/18.
- Convert m/s to km/h by multiplying by 18/5.
- Bridge length = speed × time − train length.
- Train length = speed × time − bridge length.
- For crossing a pole or person, use only the train length as the distance.
Train Crossing a Bridge FAQs
What is the train crossing a bridge formula?
Time = (train length + bridge length) ÷ train speed. Use metres and metres per second, or kilometres and kilometres per hour consistently.
A 200 m train crosses a 300 m bridge at 90 km/h. How much time does it take?
90 km/h = 25 m/s. Total distance = 200 + 300 = 500 m, so time = 500/25 = 20 seconds.
A train crosses a 250 m bridge in 15 seconds at 72 km/h. What is the train’s length?
72 km/h = 20 m/s, so total distance = 20 × 15 = 300 m. Train length = 300 − 250 = 50 m.
A 150 m train crosses a bridge in 20 seconds at 54 km/h. Find the bridge length.
54 km/h = 15 m/s. Total distance = 15 × 20 = 300 m, so bridge length = 300 − 150 = 150 m.
Why is the train length added to the bridge length?
The front of the train reaches the far end of the bridge before the rear leaves the near end. Hence, the train travels the bridge length plus its own length.
Can speed in km/h be used directly with lengths in metres?
No. Convert the speed to m/s using speed × 5/18, or convert the distance to kilometres before calculating time.