Unit conversion, relative speed, boats and streams, and the average-speed trap that catches more students than any other single idea in this topic.
Every speed problem starts with getting units right. Speeds are given in km/h or m/s, and mixing them up is the single most common source of errors in this topic.
These are reciprocals of each other, so only one needs to be memorised — the other is just its flip. 1 km/h = 1000 m / 3600 s = 5/18 m/s.
km/h is the bigger-sounding unit, so converting to the smaller m/s should give a smaller number — multiplying by the fraction 5/18 (less than 1) does exactly that.
When two objects move together, their relative speed depends entirely on whether they move in the same direction or opposite directions.
This single distinction underlies every train-crossing, boat-crossing and two-body problem in this topic.
If two objects are chasing each other in the same direction, only the gap in their speeds matters (subtract). If they're heading toward each other, both speeds contribute fully to closing the distance (add).
Boats-and-streams problems are just relative speed in disguise, where the "current" plays the role of the second moving object. Average speed problems, meanwhile, are the most commonly miscalculated question type in this entire topic.
The average speed formula is NOT the simple average of the two speeds — this is the single most common mistake in this whole topic. Simply averaging 40 and 60 gives 50, but the correct answer is 48.
Whenever a question gives two different speeds over the same distance, resist averaging them directly. Use 2xy/(x+y) instead — it always gives a value closer to the slower speed, since more time is spent travelling slowly.
All 6 questions with a full answer key.
Full solutions are in the downloadable PDF above.
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