Time, Speed, and Distance

Core formulas:

Distance = speed * time
Speed = distance / time
Time = distance / speed

Average speed:

Same distance at speeds x and y:
Average speed = 2xy / (x + y)

Same time at speeds x and y:
Average speed = (x + y) / 2

Relative speed:

Opposite directions = x + y
Same direction = |x - y|

Trains:

Time to cross pole = train length / speed
Time to cross platform = (train length + platform length) / speed

Boats and streams:

Downstream speed = boat speed + stream speed
Upstream speed = boat speed - stream speed
Boat speed = (downstream + upstream) / 2
Stream speed = (downstream - upstream) / 2

Races:

If A gives B a head start of d in race length L:
Speed ratio A:B = L : (L - d)

Circular tracks:

Opposite direction meeting time = track length / (sum of speeds)
Same direction meeting time = track length / (difference of speeds)

Unit conversion:

km/h to m/s: multiply by 5/18
m/s to km/h: multiply by 18/5

Common traps:

Average of speeds is valid only when time is equal.
For equal distance, use harmonic mean.
Convert units before calculation.

Time, Speed, and Distance​

Time, Speed, and Distance