# Trains, Boats and Streams — Every Case Explained with Pictures

Source: https://skills101.in/learn/aptitude/trains-boats-and-streams — Skills101 free tutorial (Quantitative Aptitude). Updated 2026-11-09.

These are time-speed-distance questions with one twist: you must work out the **correct distance** (trains) or the **correct speed** (boats).

## Part A — Trains

### How much distance to "cross" something?

![Crossing a pole: the train travels its own length, 200 m. Crossing a 300 m platform: train length + platform length = 500 m](https://skills101.in/learn-img/aptitude/train-platform.svg)

| The train crosses… | Distance to cover |
|---|---|
| A pole, a person standing, a tree | **Its own length** |
| A platform, a bridge, a tunnel | **Train length + that length** |
| Another train | **Sum of both lengths** (with relative speed) |

> Trains are given in **km/h** and lengths in **metres**. Convert speed with × 5/18 first.

### Example 1
*A 200 m train runs at 72 km/h. How long does it take to cross a pole?*

72 km/h = 20 m/s. Time = 200 ÷ 20 = **10 seconds**.

### Example 2
*The same train crosses a 300 m platform. How long?*

Distance = 200 + 300 = 500 m → 500 ÷ 20 = **25 seconds**.

### Example 3
*A train crosses a pole in 15 seconds and a 150 m bridge in 25 seconds. Find its length and speed.*

The extra 10 seconds are for the extra 150 m → speed = 15 m/s (= 54 km/h). Length = 15 × 15 = **225 m**.

### Two trains

Use **relative speed** (add for opposite directions, subtract for the same direction) and the **sum of their lengths**.

### Example 4
*Two trains, 150 m and 100 m long, run in opposite directions at 50 km/h and 40 km/h. How long do they take to cross each other?*

Relative speed = 90 km/h = 25 m/s. Distance = 250 m → **10 seconds**.

### Example 5
*A 120 m train at 60 km/h overtakes a man running at 6 km/h in the same direction. How long does it take to pass him?*

Relative speed = 54 km/h = 15 m/s → 120 ÷ 15 = **8 seconds**.

## Part B — Boats and streams

![A river flows one way: going with it (downstream) speed = b + s; against it (upstream) speed = b − s](https://skills101.in/learn-img/aptitude/boats-streams.svg)

- **Downstream** (with the current): **b + s**
- **Upstream** (against the current): **b − s**

where b = speed of the boat in still water, s = speed of the stream.

> **b = (downstream + upstream) ÷ 2**     **s = (downstream − upstream) ÷ 2**

### Example 6
*A boat goes 30 km downstream in 2 hours and comes back upstream in 3 hours. Find the boat's speed and the stream's speed.*

Downstream = 15 km/h, upstream = 10 km/h → b = **12.5 km/h**, s = **2.5 km/h**.

### Example 7
*A man rows at 8 km/h in still water. The river flows at 2 km/h. He takes 4 hours to row to a place and back. How far is the place?*

Down = 10, up = 6. D/10 + D/6 = 4 → (3D + 5D)/30 = 4 → D = **15 km**.

### Example 8
*A swimmer takes twice as long to swim upstream as downstream for the same distance. Find the ratio of his speed in still water to the stream's speed.*

Time up = 2 × time down → speed down = 2 × speed up. b + s = 2(b − s) → b = 3s → **3 : 1**.

## Common mistakes

- Forgetting to add the platform length.
- Not converting km/h to m/s before dividing metres.
- Adding the speeds of two trains going in the **same** direction.
- Swapping upstream and downstream: downstream is always the faster one.

## Quick recap

- Pole/person → own length. Platform/bridge → both lengths. Two trains → both lengths, relative speed.
- Downstream b + s, upstream b − s.
- b = (D + U)/2, s = (D − U)/2.


Practice quiz and free certificate: https://skills101.in/learn/aptitude/trains-boats-and-streams