Quantitative Aptitude
Time, Speed & Distance
Time, Speed & Distance
Speed, Distance, and Time are related by one fundamental equation. All TSD problems — trains, boats, races — are variations on this single relationship combined with relative speed logic.
Key Idea
Average speed for equal distances is the harmonic mean (2S1S2)/(S1+S2) — NOT the arithmetic average. This is the most common trap in TSD questions.
Core Formulas
Fundamental Relationship
Speed = Distance / Time (Distance = S × T, Time = D / S)
Always — this triangle connects all three values.
Average Speed (equal distances)
Avg Speed = 2 × S1 × S2 / (S1 + S2)
When a journey is split into two equal-distance halves at different speeds.
Relative Speed
Same direction: |S1 − S2| | Opposite direction: S1 + S2
For trains crossing, overtaking, or two objects moving towards/away from each other.
Train crossing platform
Time = (Length of Train + Length of Platform) / Speed of Train
When a train completely crosses a stationary platform or another train.
Boats & Streams
Downstream = Boat + Stream | Upstream = Boat − Stream | Boat speed = (D + U) / 2 | Stream = (D − U) / 2
For any problem involving a boat moving with or against a river current.
Relevant Exams
TSD is one of the most tested topics in SSC CGL, RRB NTPC, and UPSC CSAT — typically 3–5 questions per paper across trains, boats, and average speed variants.