Introduction
Time, Speed and Distance (TSD) is the foundation chapter for Boats & Streams and Trains — master the
core formula and unit conversions here, since both later chapters are direct applications of these same
rules.
Core Formula
| Formula |
|---|
| Speed = Distance / Time |
| Distance = Speed × Time |
| Time = Distance / Speed |
Unit Conversion — Memorise This
Flowchart — km/h ↔ m/s Conversion
km/h → m/s: multiply by 5/18
↔
m/s → km/h: multiply by 18/5
Q. Convert 72 km/h into m/s.
72 × (5/18) = 20 m/s
Average Speed Formula (Key Trap Area)
⚠️ Common Trap: Average speed is NOT simply the average of the two speeds — that only works if the time (not distance) is equal for both parts.
| Scenario | Formula |
|---|
| Equal distance, different speeds (v₁, v₂) | Average Speed = 2v₁v₂ / (v₁+v₂) |
| Equal time, different speeds | Average Speed = (v₁+v₂) / 2 (simple average works here) |
Q. A car covers a certain distance at 40 km/h and returns the same distance at 60 km/h. Find the average speed for the whole journey.
Average Speed = 2×40×60 / (40+60) = 4800/100 = 48 km/h
Relative Speed
| Scenario | Relative Speed |
|---|
| Moving in the same direction | Difference of speeds (v₁ − v₂) |
| Moving in opposite directions | Sum of speeds (v₁ + v₂) |
Q. Two cars start from the same point and move in opposite directions at 50 km/h and 70 km/h. After how much time will they be 360 km apart?
Relative speed (opposite direction) = 50+70 = 120 km/h
Time = 360/120 = 3 hours
"Meeting Point" and "Same Time, Different Point" Patterns
Q. A and B start walking towards each other from two points 100 km apart, at speeds of 6 km/h and 4 km/h respectively. After how much time will they meet?
Relative speed = 6+4 = 10 km/h
Time to meet = 100/10 = 10 hours
💡 Exam Tip: Always convert every speed to the same unit (usually km/h or m/s) before applying any formula — mixing units is the most common source of error in this chapter.
✅ Practice Focus: km/h ↔ m/s conversion (5/18, 18/5) · Average speed formula for equal-distance journeys (2v₁v₂/(v₁+v₂)) · Relative speed — same vs opposite direction · Meeting-point time calculation.