SATHEE: Time Speed Distance Formulas

Time Speed Distance Formulas - Quick Revision

Distance = Speed × Time (DST triangle: cover the one you need)
Always convert units first: km/h → m/s multiply by 5/18; m/s → km/h multiply by 18/5
Average speed = Total Distance ÷ Total Time (never add speeds directly)
Relative speed for same direction: subtract speeds; opposite direction: add speeds
Meeting time = Initial gap ÷ Relative speed
Upstream speed = Boat speed – Stream speed
Downstream speed = Boat speed + Stream speed
Train crossing pole: distance = train length
Train crossing platform/bridge: distance = train length + platform length
Two trains crossing (opposite): relative speed = sum of speeds
Two trains crossing (same direction): relative speed = difference of speeds
Circular track 1st meeting: time = track length ÷ relative speed
Circular track 1st meeting at starting point: LCM of individual lap times
If speed changes in ratio a:b, time changes in ratio b:a for same distance
1 km/h ≈ 0.28 m/s; 1 m/s ≈ 3.6 km/h
Speed of 60 km/h = 1 km/min = 16⅔ m/s

Formula/Rule	Application
Speed = Distance / Time	Compute speed when distance & time known
Time = Distance / Speed	Compute time when distance & speed known
Average speed (equal distances) = 2ab/(a+b)	Two legs at speeds a & b
Relative speed (opposite) = v₁ + v₂	Objects moving towards each other
Relative speed (same direction) =	v₁ – v₂
Boat speed in still water = (Down + Up)/2	Find boat’s own speed
Stream speed = (Down – Up)/2	Find current’s speed
Circular track nth meeting time = nL / relative speed	When runners meet again
% change in time = (100 × (new speed – old speed)) / new speed	Speed ↑ 25% ⇒ time ↓ 20%

DST-triangle: Draw Δ, write D-S-T at corners; cover the unknown → formula revealed.
“Up-minus, Down-plus” – Upstream subtracts stream, Downstream adds stream.
“5 to 18, 18 to 5” – Sing it like a rap to remember unit-conversion factor.
“Pole is a point” – Crossing pole ⇒ distance = train length only.
“Same minus, Opposite plus” – Relative-speed sign rule.

Mistake	Correct Approach
Adding speeds directly for average speed	Use Total Distance ÷ Total Time
Forgetting unit conversion (km/h vs m/s)	Convert first: 1 km/h = 5/18 m/s
Using train length only for platform	Add train + platform lengths
Taking relative speed as sum in chasing	Subtract speeds (same direction)
Calculating % time change wrong	Time ratio is inverse of speed ratio

1. A 200 m train at 20 m/s crosses a 300 m platform. Time taken?

Distance = 500 m; Time = 500/20 = 25 s

2. A man rows 18 km downstream in 1½ h. If stream speed = 6 km/h, find upstream speed.

Down = 18/1.5 = 12 km/h → Boat = 12 – 6 = 6 km/h → Up = 6 – 6 = 0 km/h (he can’t row upstream)

3. By increasing speed 25%, time reduces by how many %?

25% ↑ speed ⇒ 20% ↓ time

4. Two trains (lengths 150 m & 200 m) run opposite at 60 km/h & 40 km/h. Crossing time?

Relative = 100 km/h = 250/9 m/s; Total dist = 350 m; Time = 350×9/250 = 12.6 s

5. Runner A laps in 90 s, B in 120 s on 600 m track. When do they 1st meet at start?

LCM(90,120) = 360 s = 6 min