Introduction
Speed = Distance ÷ Time. This core relationship, combined with unit conversion and relative motion, forms the
base for three related chapters that follow: Boats & Streams, and Problems on Trains.
Core Formulas
| Concept | Formula |
|---|
| Unit conversion | km/hr to m/s: multiply by 5/18. m/s to km/hr: multiply by 18/5. |
| Relative speed (same direction) | Difference of speeds |
| Relative speed (opposite direction) | Sum of speeds |
| Average speed (equal distances, two speeds) | 2×S1×S2 / (S1+S2) |
Q. A train's speed is 72 km/hr. Convert this to m/s.
72 × 5/18 = 20 m/s.
Q. Two cars start from the same point and travel in opposite directions at 60 km/hr and 40 km/hr. After how much time will they be 200 km apart?
Opposite direction → relative speed = 60+40 = 100 km/hr. Time = Distance/Speed = 200/100 = 2 hours.
Q. A covers a distance at 40 km/hr and returns the same distance at 60 km/hr. Find his average speed for the whole journey.
Average speed = 2×40×60 / (40+60) = 4800/100 = 48 km/hr (not the plain average of 50).
⚠️ Key Insight: The average speed formula 2×S1×S2/(S1+S2) applies only when the two distances
covered are equal — for unequal distances, use Total Distance ÷ Total Time directly.
💡 Exam Tip: Memorise the 5/18 and 18/5 conversion factors cold — nearly every speed-distance
question in banking mixes km/hr and m/s, and hesitating here costs valuable seconds.
✅ Practice Focus: Unit conversion · Same-direction vs opposite-direction relative speed ·
Average speed for equal-distance trips · Races and head-starts.