Fundamentals of Business Mathematics and Statistics · Time and Distance

Problems on Trains: Time and Distance for CMA Foundation

Updated 10 October 2026 · Fact-checked

A train problem is a time and distance problem where the train's own length matters. To cross an object, the train covers its own length plus the object's length. Use time = distance ÷ speed. For two trains, use relative speed: add speeds if opposite, subtract if same direction.

Understand Problems on Trains

A train problem is a normal speed, distance and time problem with one twist: a train is long, so you cannot treat it as a point. You must decide what distance the train actually covers.

When a train crosses a pole, a tree or a standing person, only the front of the train has to reach the pole and the tail has to clear it. So the distance covered is just the length of the train.

When a train crosses a platform or a bridge, the engine enters at one end and the last coach must leave the other end. The distance covered is length of train + length of platform (or bridge).

When two trains cross each other, think of one train as standing still and the other moving at the relative speed. The distance is the sum of both lengths. If the trains move in opposite directions, the speeds add. If they move in the same direction, the speeds subtract (faster minus slower).

Finally, watch units. Train speeds are usually in km/hr, while lengths are in metres and times in seconds. Convert km/hr to m/s by multiplying by 5/18.

Key formulas to remember

Basic relation: Time = Distance ÷ Speed; Keep distance and speed in matching units (metres with m/s, km with km/hr).
Train crossing a pole or standing person: Distance = Length of train; Time = length of train ÷ speed of train.
Train crossing a platform or bridge: Distance = Length of train + Length of platform; The same rule applies to bridges and tunnels.
km/hr to m/s: x km/hr = x × 5/18 m/s; Example: 72 km/hr = 72 × 5/18 = 20 m/s.
m/s to km/hr: y m/s = y × 18/5 km/hr; Example: 10 m/s = 36 km/hr.
Two trains in opposite directions: Relative speed = S1 + S2; Time to cross = (L1 + L2) ÷ (S1 + S2).
Two trains in the same direction: Relative speed = S1 − S2 (S1 > S2); Time to cross = (L1 + L2) ÷ (S1 − S2).
Train passing a moving person: Relative speed = train speed ± person speed; Subtract if moving the same way, add if moving opposite. Distance is the train's length only.

How to solve Problems on Trains questions

Use this same routine for every train question. It stops you from mixing up distances and units.

1Read the question and list what is given: lengths, speeds, times.
2Identify what the train crosses: a pole or person (length only), a platform or bridge (length + length), or another train (both lengths).
3Decide the speed to use: the train's own speed, or the relative speed if another moving body is involved.
4For two moving bodies, add speeds if they move in opposite directions and subtract if in the same direction.
5Convert all units so they match. Usually change km/hr to m/s with × 5/18.
6Write Distance = Speed × Time and substitute the values.
7Solve for the unknown (length, speed or time).
8Check that the answer is sensible and in the unit the question asks for.

Quickest way: Convert once, then think in metres and seconds

When to use it: Use when the speed is in km/hr but lengths are in metres and time in seconds, which is the most common exam setup.

Convert speeds to m/s at the start. Memorise 36 km/hr = 10 m/s, 54 = 15, 72 = 20, 90 = 25.
Write the total distance in one line, for example L + 200.
Use total distance = speed × time directly.
For options, estimate first. If the answer must be 20 × 15 = 300, you can reject options far from that.
For same-direction or opposite-direction trains, find the relative speed first, then multiply by the time to get the sum of lengths.

Common mistakes in Problems on Trains

Using only the train's length when crossing a platform.
Students remember the pole case and apply it everywhere.
Fix: For platforms and bridges, always write distance as train length + platform length.
Forgetting to convert km/hr to m/s.
The question mixes units and students plug numbers straight in.
Fix: Convert speed first using × 5/18 before writing any equation.
Adding speeds for trains moving in the same direction.
Students remember 'relative speed' but not which operation applies.
Fix: Opposite directions: add. Same direction: subtract. Picture one train chasing the other.
Using only one train's length when two trains cross.
Students focus on the train they are asked about.
Fix: When two trains cross each other, the distance is L1 + L2.
Adding the platform length when a train passes a person on the platform.
The word 'platform' triggers the platform formula.
Fix: A person standing on the platform is a point object, so the distance is only the train's length.
Converting m/s to km/hr with 5/18 instead of 18/5.
Students mix up the two conversion factors.
Fix: Remember that km/hr numbers are bigger than m/s numbers, so m/s to km/hr multiplies by 18/5.

Worked examples

Example 1

A train 150 m long running at 54 km/hr crosses a platform in 30 seconds. Find the length of the platform.

Show the solution

Speed = 54 × 5/18 = 15 m/s.
Distance covered in 30 seconds = 15 × 30 = 450 m.
This distance = length of train + length of platform.
So platform length = 450 − 150 = 300 m.

Answer: 300 m

Example 2

Two trains of lengths 120 m and 180 m run on parallel tracks in opposite directions at 60 km/hr and 48 km/hr. How many seconds do they take to cross each other?

Show the solution

Relative speed = 60 + 48 = 108 km/hr.
Convert: 108 × 5/18 = 30 m/s.
Total distance = 120 + 180 = 300 m.
Time = 300 ÷ 30 = 10 seconds.

Answer: 10 seconds

Exam tips

Before calculating, ask what the train crosses. This one decision sets the distance and decides most of the marks.
Learn the pairs 36→10, 54→15, 72→20, 90→25 m/s so conversions take seconds.
With no negative marking, always attempt every train question. Even a quick estimate can eliminate two options.
If a question gives the time to pass a pole and the time to cross a platform, use the pole time to find the train's length or speed. Then subtract to get the platform length.
Check the unit asked in the options: metres, seconds or km/hr.

Practice questions from Time and Distance

Problems on Trains: frequently asked questions

How do I find the time a train takes to cross a platform?

Add the length of the train and the length of the platform to get the distance. Convert the speed to m/s if lengths are in metres. Then divide distance by speed.

What is the formula for two trains crossing each other?

Time = (L1 + L2) ÷ relative speed. For opposite directions the relative speed is S1 + S2. For the same direction it is the difference of the speeds.

Why do we multiply by 5/18?

1 km is 1000 m and 1 hour is 3600 seconds. So 1 km/hr = 1000/3600 = 5/18 m/s.

Is the length of the train needed to cross a pole?

Yes. The train must travel its own length to pass the pole completely. So the time is length divided by speed.