Trains, Boats and Streams

Why this topic is a guaranteed scorer

In AFCAT, every correct answer earns +3 and every wrong one costs −1. With 250+ marks on offer and a tight clock, you cannot afford to lose time on topics that should be automatic. Trains, Boats and Streams is exactly such a topic: the question types repeat year after year, and the maths rarely goes beyond simple arithmetic. A candidate who has drilled these patterns can finish a question in the time another candidate spends merely reading it.

The reason this topic feels intimidating to beginners is the wording, not the mathematics. Phrases like “crosses a platform”, “overtakes”, “rows against the current” sound complicated, but each one simply tells you two things: what distance is covered and which speed to use. Once you train your eye to extract those two pieces, the answer drops out of the master formula every single time.

The whole chapter rests on one master relation. If you internalise it and the two or three derived formulas, you can answer almost any question by inspection rather than by lengthy working.

Throughout this guide, treat trains and boats as two sides of the same coin. Trains add or subtract speeds because of direction of travel; boats add or subtract because of the current. The arithmetic is identical — only the story changes.

The unit conversion that decides your speed

Train and boat questions mix km/h with metres and seconds. Getting the conversion wrong is the single biggest reason candidates lose marks here, so memorise both directions until they are automatic. Examiners deliberately set the time in seconds and the speed in km/h precisely to catch the unwary.

Why 5/18? Because 1 km = 1000 m and 1 hour = 3600 s, so 1 km/h = 1000/3600 = 5/18 m/s. Keep this as a reflex rather than re-deriving it in the hall. A neat way to remember which fraction goes which way: the bigger unit (km/h) becomes the smaller number (m/s), so you multiply by the smaller fraction, 5/18.

A second reason to be careful is that lengths almost always arrive in metres while many speeds arrive in km/h. The moment you see a train length in metres and a time in seconds, your instinct should be to put the speed into m/s before doing anything else. Train your hand to write the conversion first, so it never gets forgotten halfway through.

What a train actually has to cross

The trick with trains is realising that a train is not a point — it has length. The front of the train reaches the object first, but the train has only finished crossing when its rear clears the object too. The distance it covers while crossing something therefore depends on what that something is.

So time to cross a pole = (length of train) ÷ speed, while time to cross a platform = (length of train + length of platform) ÷ speed. Always ask one question: does the object have length?

Picture it physically. To pass a thin pole, the train moves forward by exactly its own length — the front passes the pole, then the rest of the carriages follow until the last coach is gone. To pass a 200 m platform, the front must travel the full 200 m of platform plus the train length so that the rear finally steps off the far end. That extra length is the whole game.

Relative speed for two trains

When two trains interact, you compare their speeds. The direction decides whether you add or subtract.

Why does direction flip the sign? When two trains move towards each other, the gap between them closes at the combined rate, so their speeds add. When one chases the other in the same direction, the faster train only gains on the slower one at the difference of their speeds, so you subtract. This is the heart of every relative-motion question, and it applies to people walking, cars driving and boats rowing just as much as to trains.

A handy result: if two trains of equal length take t₁ and t₂ seconds to pass a pole, and T seconds to cross each other while moving opposite, the lengths and speeds can all be linked back to the master formula. In the exam, you rarely need that full algebra — just plug numbers into sum-of-lengths over relative-speed and you are done.

Worked example: two trains crossing

Boats and streams: the core pair

Now switch to water. A boat has its own speed in still water, but the river current (stream) either helps or fights it.

From these two, the two most useful reverse formulas fall out instantly:

It helps to see why these two reverse formulas are true. Add the downstream and upstream speeds: (b + s) + (b − s) = 2b, so dividing by 2 isolates the boat speed b. Subtract them: (b + s) − (b − s) = 2s, so half the difference gives the stream speed s. No memorisation tricks needed — the algebra is two lines long and you can rebuild it any time you blank out.

The same b-and-s pair handles swimmers in a river, an aircraft flying with or against the wind, and a man walking on a moving escalator. The “stream” is just any helping or opposing background speed. Recognising this lets you reuse one method across several disguised question types in the paper.

Worked example: finding boat and stream speed

Notice you never needed to set up algebra. Find the two speeds, then take the average and half-difference.

The round-trip and average-speed traps

A favourite AFCAT trick is the same-distance round trip: a boat goes downstream and returns upstream over the same distance. The average speed for the whole trip is not the simple average of the two speeds. The reason is timing — the boat crawls upstream and so spends far longer at the slow speed than at the fast one, which drags the true average down below the midpoint.

Traps that cost AFCAT candidates marks

• Unit clash: mixing km/h with metres. Convert before you compute, not after.
• Forgetting object length: a bridge or tunnel adds to the distance; a pole does not.
• Wrong sign for stream: downstream adds, upstream subtracts. Re-read the direction.
• Equal-length assumption: two trains are not always the same length — read carefully.
• Average-speed slip: round trips use the harmonic mean, never the plain average.

Previous-year style practice

This is the exact shape of most AFCAT train questions: a length, a platform, a time, and one conversion at the end. Notice the discipline — add the two lengths first, divide by time to get m/s, and only then convert to km/h because the options were in km/h. Reverse the order and you will still arrive at the same answer, but doing it in this sequence keeps your units clean and your mind calm under the clock.

Boat questions follow an equally fixed template: a downstream time, an upstream time, and a request for either the boat speed, the stream speed, or a total journey time. Spot which of the three is being asked, reach for the matching one-line formula, and you will almost never need to write a system of equations.

Cavalier speed strategy in the exam hall

To turn knowledge into marks under time pressure, follow a fixed routine for every question:

1. Read the direction words (towards, same, downstream, upstream) and circle them.
2. Decide: do I add or subtract speeds?
3. Decide: does the object have length to add to the distance?
4. Match units — convert once if needed.
5. Apply the master formula and pick the option.

Quick revision