Time, Speed, Distance: Complete Guide

Basic Formulas

• Distance = Speed × Time
• Speed = Distance / Time
• Time = Distance / Speed

Unit Conversions

• 1 m/s = 18/5 km/hr = 3.6 km/hr
• 1 km/hr = 5/18 m/s

Relative Speed

• Same direction: Relative speed = |S₁ - S₂|
• Opposite direction: Relative speed = S₁ + S₂

Trains

• Crossing a pole/person: Time = Length of train / Speed
• Crossing a platform: Time = (Length of train + Length of platform) / Speed
• Two trains crossing: Time = (L₁ + L₂) / Relative 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

Average Speed

• For equal distances: Average = 2ab/(a+b) (harmonic mean)
• For equal times: Average = (a+b)/2 (arithmetic mean)

CAT Tip

Always check units - most errors come from mixing km/hr and m/s.