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Why One Idea Solves Three Chapters
Trains crossing poles, trains crossing each other, and boats moving with or against a river look like three separate chapters. They are one idea: relative speed. When two things move towards each other, the gap closes at the sum of their speeds. When they move the same way, the gap closes at the difference. A boat in a river is exactly this — the water is a second moving thing, and it either helps the boat or fights it.
Before any formula, fix the units. Distances in these questions are usually in metres (train lengths) while speeds are in km/h. The bridge between them is:
km/h → m/s: multiply by 5/18
m/s → km/h: multiply by 18/5
Example: 72 km/h = 72 × 5/18 = 20 m/s. Most wrong answers in this chapter are not wrong formulas; they are a speed in km/h divided into a distance in metres. Convert first, always, and the rest is one division.
1. Express 72 km/h in metres per second.
2. A 200 m long train running at 36 km/h crosses a telegraph pole. How long does it take?
3. A 300 m train moving at 72 km/h crosses a 500 m long platform. The time taken is:
4. Two trains 120 m and 130 m long run on parallel tracks in opposite directions at 40 km/h and 60 km/h. How long do they take to cross each other?
5. A boat goes downstream at 18 km/h and upstream at 10 km/h. What is the speed of the stream?
6. A boat whose speed in still water is 8 km/h goes 30 km downstream and returns. If the stream flows at 2 km/h, the total time is:
7. A boat covers 24 km downstream in 2 hours and the same distance upstream in 3 hours. What is its speed in still water?
8. A car travels from A to B at 40 km/h and returns along the same road at 60 km/h. Its average speed for the whole journey is: